Hello tuba father from Sacramento!
Our son (now HS freshman) did the same path, except he came from clarinet via bass clarinet and trombone to tuba. Initially, he played on the middle-school owned Jupiter 3/4 size 3-valve. Then we rented a really crappy old Conn 3/4 tuba for a summer. When he started having lessons with a real tuba teacher, it very quickly became clear that a 3/4-size 3-valve student instrument (in particular one that's badly made or beat up) is not a good place to learn on. Or to quote his teacher: "A professional would have a hard time making beautiful music on that piece of crap. How can you expect a student to learn on it?" We were lucky to find a Meinl-Weston 25 for our son (4-valve BBb, slightly bigger than the Miraphone 186, which is the gold standard of 4-valve instruments), which he played the heck out of for several years. Recently, he was upgraded to a 5-valve CC horn. Unfortunately, our MW 25 won't be for sale anytime soon, as it is being used as a loaner instrument for others right now.
I think 4 valves is a de-facto requirement, even for the middle school repertoire. The intonation of the low notes is just too awful with the 1+3 combination. Maybe a experienced player could overcome that (with slide pulling), but a 13-year old should not be expected to have to deal with those complications. Plus, in high school she'll be playing a 4-valve horn anyhow (except for those sousaphones in marching band, but there the sound is secondary, and looking good is where it's at).
What would the collective wisdom recommend?
Second mortgage? Just kidding!
Here's my advice: Go for a solid, name-brand instrument. Don't worry about it being old and beat up. A few years of school, and it will be a lot more old and beat up, as long as it plays well. And with tubas being dent-magnets, you will be taking it to the repair shop more frequently than you want to, so why invest in something shiny at the beginning.
Fortunately, you have a good shop in Sacramento: Tim's Band Instruments (the technician there is called Scott). Professionals from the bay area take their instruments on a 3-hour drive to Sacto when our own local repair guru is backlogged. I would start by going over there and getting advice, and see what they have in used gear. And then I would look both in the for-sale section here, and on Craigslist. Also look at the website of The Horn Guys. They're the best (and largest) tuba store on the west coast, located in LA. They might have an instrument for you, and with a weekend trip down there you can save a bit of shipping cost, and maybe combine it with a visit to Disney.
For example, look around for a Miraphone 186 (or it's slightly smaller cousin, the 184), or the Meinl-Weston equivalent, or the King 2341 or its Conn equivalent, or (if you are into top-valves) the Yamaha 321 (or its Holton clone). With a little patience, you'll find a used instrument in the right price range. Chinese clones (often sold under western-sounding names) are a two-edged sword. When we were looking for our most recent tuba, we tested a Chinese clone that was completely awful, stuffy (in spite of having large pipes!) and with horrible intonation. But we've also recently seen some very good Chinese (and Russian) instruments that played fine. Our neighboring middle school had a St. Petersburg 4/4 BBb 4-valve that played very nicely, and looked sturdy. Repair parts for Chinese instruments: One does worry about that, although a good technician can improvise amazing things. But consider that for many established brands, getting parts isn't always trivial or fast either (in particular the ones that have to come across the ocean).
In all that, don't forget the cost of shipping. I've bought an instrument from Bloke (and highly recommend him!) for our middle school, but don't forget that he's in the southeast and you are in the west, and the Greyhound bus will take a long time and a bit of money to get a tuba to you. If you can find one locally, so much the better.
Ok, here is a question Im sure everyone is sick of answering...bear with me: piston vs rotary? Do rotary take wear better (last longer), sound different, or other?
Welcome to the #1 religious debate. They have pluses and minuses. Pistons are easier to clean and do simple maintenance on. They are harder to repair if something gets bent, but they are sturdier and don't get damaged so much. Rotaries can be a little finicky, but a musically and mechanically talented parent can do a lot of adjustment and repair themselves. I think rotaries are easier to learn on (because they sound more "accurate", and you don't get funny noises from half-pressed valves), and can be harder to master for advanced students (because they can be a bit slower, and interrupt the airflow more when playing legato). Our son's teacher generally recommends rotaries for his students, if there is a choice, and mostly plays rotary instruments himself. Another fine tuba professional in the area swears by pistons. Our son has played them both, and when we bought his new tuba, he insisted on a rotary horn, since he wants the accuracy of the rotors, even though he knows that he can fake super-fast passages on the pistons better (but neither his teacher nor his band director would let him get away with faking).
As a total beginner, your daughter's opinion in this matter will (unfortunately!) not matter much. Here's my advice: She will, sooner rather than later, need a private teacher anyhow, if she's serious about playing. Go ask that teacher for their advice, not just on rotary-versus-piston, but on generally which tuba to pick. And ask that teacher to try out candidate horns, in particular used and beat up ones.
There is also one other issue: physical size. If your daughter is tiny, then tuba might just not be the right choice for her. In my son's high school, there is a petite freshman lady (70 lbs!) who has decided that she really wants to play tuba, and she has a hard time. We even lent her a playing stand (so she doesn't have to balance the horn on her lap), but it seems to just not be working out. I think the problem is partly embouchure and lung volume, and partly that just balancing the horn requires 110% of her strength and attention, not leaving much for playing. Fortunately, she is a very fine woodwind player, and going back to that will not be seen as a defeat. On the other hand, once holding and balancing the instrument is taken care of, one doesn't do a student a favor by putting them on a hard-to-play tiny horn. In middle and high school, I've seen several smallish students handle tubas just fine, and sound great.
One last issue, unfortunately an important one: If you buy a horn, and it is at home for practice, what will your daughter play at school? Life during the daily band class will be miserable on a crappy student 3-valve horn, if she has a nice 4-valve horn at home. You may end up being like me, with a giant hard-case for a horn in the back of the car every morning.
Good luck! If you're ever in the San Jose / Los Gatos area, come on by. Or arrange for your daughter to have a lesson with our son's teacher (he's not only a great tuba player, but also a fabulous teacher).
