Some semi-random answers to your questions:
The biggest problem with the switch is the cost of the instrument. Even if you have a supplied horn, cost factors are going to enter into the switch at each and every level:
• The hardware is where it all starts. At the very most basic level, a decent student clarinet can be had for a couple of hundred bucks. A decent bass clarinet is going to run you some multiple of that, probably five or so.
While a bass is a bit more complicated in design than a soprano, the main factor here is the size of the instrument. Double the length, but volume varies by the cube root. So, you've got greater surface area to finish and detail, and all of that there. While labor is probably the greatest expense in creating either horn, there is the perceived value issue, where a manufacturer sets a price by what the producer thinks the purchaser would pay.
In any event, they are bigger. Bigger reeds are the first result of this. (Bigger swabs, too.) Round these parts, the reeds (even bassoon reeds) are supplied by the schools, but when I was a young tad, you bought your own. Ouch!
Big also means orthometric problems. Little bodies are not particularly suited to playing the bass clarinet. The finger stretch on a soprano is sometimes too much for the slight player, as is the flat neck angle with which most entry level basses are sold. This may rule out bass clarinet playing for some, although most everyone grows into a suitable size.
But, the real kicker is the big maintenance costs. I just got my principal bass clarinet (a Selmer Model 33 extended range horn) re-regulated. (We're in show season here, and I'm playing two bass clarinet intensive books, Cinderella and a rewrite of Annie Get Your Gun, which actually employs the extended range notes), and it was almost time for the semi-annual tune up anyway. Total cost out the door, with no new pads and only a cork or two replaced, was $52.00.
Not many parents (and even fewer school districts) would look favorably upon a hundred bucks per annum for instrument maintenance. I spend about twice the amount on the bass as I do on my baritone each year, most of it attributed to those saucer pads on the lower joint.
The trouble is that most schools (and parents) are not willing to invest the extra money to keep one of these larger (and much more vulnerable) instruments in good working order. As the precise area that these pads are located in is also the most vulnerable to contact with chairs and the like, they are frequently "dinged" just enough to make playing a bass over the break a trial once the damage is done.
With my bass students back in the 1980's, the main problem that they faced was this damage to the large pads on the lower joint. I had the parents commit to the purchase of a student bass before I would take their child on as a student. (Most were comfortably middle class or higher, and had no problem with the expense.) If they did not do this, I politely sent them on their way.
In each and every case, a student who was going through agonies playing on a school bass clarinet "took off" like a rocket once they had an instrument that was protected from the typical kind of abuse that any school horn gets; the trip over the break was no longer a challenge. (One particularly dedicated student was actually in tears when she first tried her new horn.)
This maintenance cost issue comes into play in another way, for many bass clarinets available for purchase are ex-school horns, and have thus lived a very hard life. Look at some of the auctions on eBay for second hand basses, and you will see what I mean. Getting this fixed is a cost that needs to be built into the horn - don't count on getting a flawless instrument. (They never come that way from the factory, either.)
° Technologically speaking, when you purchase a soprano clarinet, you end up with the "bog standard" Klóse Boehm soprano, the same as what has been produced for French style clarinet players for the last century and a half. Indeed, it's hard to purchase anything but.
With bass clarinets, it's a bit different. Horns below the professional level are going to come with the "on the body" register key assembly (except for those from China). This "simple system" throws one tone hole open for Bb in the staff, and another for everything in the clarinet register and above.
This works, but the sad truth is that trying to get a good clean sound out of that single "on the body" register key opening causes less than optimal production of some of the notes to which it is applied. (Oddly enough, this "simple system" is an improvement for the Bb.)
(Not everyone feels this way, but I would submit that the preference that some show for this register mechanism is usually shaped by the fact that it is the mechanism available to them. In effect, they make do.)
WIth the other register mechanism (the "on the neck" vent one), you still have two tone holes operated by the register key. However, one opens for the notes running from Bb on up to D in the staff, whereupon the second hole is automatically substituted. This makes for a much smoother transition from the lower range to the higher one, although the "simple system" often has a better sounding Bb.
However, the "on the neck" register system is much more susceptible to damage. There is a lot of linkage and rods and little flippy parts on these horns that makes this all happen. On an aging Kohler bass clarinet with this type of system, the day-to-day school use often leaves it broken or at least sadly out of regulation. And, on a horn with less than quality keywork (think Chinese here), the long rods involved (a total of about a foot and a half of axle key) are far too easily bent, even just when handling the horn in and out of the case.
For someone in school, I would be hesitant to recommend anything but the "simple" register key mechanism. And, the manufacturers seem to agree with me - I'm glad I got something right. For an adult (or a serious high school student or a very serious junior high student, the "on the neck" system should work just fine.
(What about the problem with the throat Bb? This is where that second trill key from the top is your best friend. For quarter notes and longer, play the throat Bb with this key and the A key, and all will be fine. I am amazed that more do not follow this system, but there you go - there's nought like folk.)
The time to step up to a "professional" instrument is upon taking up a music degree in college. Before if you have the money to spend, but otherwise wait. A quality bass clarinet will set you back something in the neighborhood of $6,000 - not small change by any standard.
• What are the "joys" of bass clarinet playing? Well, they come in a number of varieties:
1) If you apply yourself on bass, you will have a much better shot at playing in higher level groups (All-State, All-County, whatever). Good clarinet players are a dime a dozen, good bass clarinet players (with properly functioning instruments) come in the dollar a dozen range.
2) On bass, you will have two instruments under your belt at a very young age. Despite what you may believe, pure clarinet playing is not all that much in demand these days. Instead, "pro" work (or even semi-pro work) will come with a "must play flute, clarinet, alto saxophone, bass clarinet" qualifier.
If your school does musicals, you will quickly find that each reed book (on anything done after the 1940's) will typically look for one person playing three or four instruments. Getting bass clarinet down now will bring you a long way towards dealing with this. (It also sort of "pre-trains" you for playing saxophone.)
3) Bass clarinet parts are often boring at the secondary school level. However, as an atmosphere instrument, the bass is only equalled by the english horn and bassoon in its application. As you start playing music at a higher level, you will find more and more of these parts cropping up. For example, Gershwin's An American In Paris suite (in the full orchestral version) has three extremely prominent bass clarinet solos, two of which can be milked for all they are worth.
4) Did I mention orchestra music? In "real" (i.e., philharmonic) school orchestras, there are usually only two clarinet players. But, in districts with more challenging programs, the director will (if given the option of a technically competent bass clarinet player) reach out to stuff like the aforementioned Gershwin piece. Better for the group, better for the player.
If you are looking to play bass in a school (or college) orchestra, you should also keep your soprano chops up to snuff. At the advanced high school level, only about one in five pieces performed will have a bass clarinet part. Most likely, you will only be called upon to sit in (rather than take the class all semester) in such circumstances.
(When I was a high schooler, my district (despite having a very highly regarded music program) did not have an orchestra. As a result, I found myself being the only kid from a school that did not have an orchestra in the All-County Orchestra. Of course, doubling on soprano and bassoon didn't hurt - you can never have too many competent bassoon players around...)
• Should you own your own?
Without question, if you want it to stay in good playing order. I can't stress this point enough - if you know what you are doing, you can get by on a school horn, but it's not something I'd want to have to do on a daily basis.
• Bass clarinet or soprano clarinet?
Ideally, both, plus flute and a saxophone. Most show books (a good part of the available pro or semi-pro income from music out there in the big bad real world) will have a Reed IV or V book with clarinet, bass clarinet and baritone saxophone. Expensive to own, but if you can handle all three, you can pretty well barge your way in and make $500 a production, as the skills set is not all that common. Our union local has a directory that has scads of clarinet and alto/tenor players, but only one tenth as many bass and baritone players. There's your musical road map, plain and simple. (The school baritone will probably be in good enough condition.)
In addition to being rewarding financially, shows are challenging (with extended sections in high flat and sharp (especially sharp) keys, exposed passages and plenty of solos for all instruments). Spend time in the orchestral pit, and you'll never want to see another concert band part.
You will probably learn sax on an alto, but it all transfers to any of the other saxes, so don't worry.