Last year I asked a the same question on tMP and got good advice. I can briefly summarize it as follows:
"Sod the small stuff"
I was worried about giving an 11 year old the senior band’s spare Sov EEb as I thought it would be too big, but on advice from tMP, gave it, and the young lad is doing great. Size wasn't the issue I thought it'd be. Also picked up an old Yamaha EEb that received a similar response.
You'll get a full size EEb bass second hand for less than the cost of a 3/4 size new, and is probably a better long term investment. You won't find yourself looking to replace it in a few years time as your players grow. I wouldn't worry, they'll adjust quickly to the size.
But if you have the cash, Jupiter, Besson, Yamaha 3/4 size are all good. Wouldn't turn down a second-hand Amati at the right price. Not great, but they're functional. As Peter was saying, Imperials are quite good and are that bit smaller than newer basses. I have my eye on one at the moment!
Student trombone-wise, we found Bach is v.good, if pricey, and is what we mostly use with our youth band. Have some King 606's which I quite
like. Have one Blessing which is average enough, but does the job. Most of the main brands are safe enough I'd imagine. Can't speak for the Elkhart or new Besson 1000 series trombones.