These are only recommendations. There are obviously many great instruments out there (and many crappy ones); I do not assume that this list is complete. I have only tried to list those that in my experience work well for middle school to early college students (which is a wide range!!).
There are basically three levels of instruments sold in most music stores: Beginner, Intermediate (or Step-up), and Professional.
The "step-up" or intermediate level instruments promoted by many music stores are usually not cost effective to purchase new. Unless you can find a good quality used "step-up" horn at a reasonable price I recommend waiting until you're ready to skip directly to an instrument most stores classify as "professional".
Mouthpieces - Trombone & Euphonium
Many beginner instruments come with a 12C mouthpiece, this is fine for the first six months to a year.
(At this point do not try to make any sense out of what '12C' means, size listings are inconsistent and confusing.)
Before purchasing a better instrument you should first get a larger mouthpiece. The usual upgrade size is a 6 1/2 AL (sometimes seen as 6.5 AL). This mouthpiece comes in both a small and large shank (6 1/2 AL-L) version and is usually what students are playing when they purchase a larger horn.
Eventually most (not all) students move from a 6 1/2 AL to a 5G on trombone. Euphonium students typically move to a Schilke 51D. After that upgrades are made on a much more individual basis.
Some other common brands and sizes are:
Bach 5GS, 4G, 3G
Schilke 51, 51D, D5.1, D5.2
Wick 4 1/2 AL, 4BL, 4AL, 5BL, 5AL, 5ABL
(most beginner instruments have a .500 inch bore and take small-shank mouthpieces, but some professional trombones have similar specs so don't let that confuse you)
Yamaha 354 - By far the best made student trombone, definitely worth the few extra months of payments. This horn will also work great when students start working on jazz.
With your first purchase please use the "toilet paper/underwear rule:" Do not buy a musical instrument anywhere you can also buy underwear or toilet paper (no matter how shiny).
I recommend that most students upgrade to an instrument with a .547 inch bore size, large shank, and that has a valve; however, occasionally a student may want a .525 bore, small or large shank. A few instruments with .525 bore (like a Bach 36) are designated as "professional" in music stores. Below I have only listed .547 horns
Bach 42 - is probably the most common trombone out there and for many this is the measuring stick. There are different options that are represented after the 42 (e.g. 42B, 42BO, 42T, LT42TGLW50). Make sure you look into what the letter after the 42 represents as just a plain 42 doesn't not have a F-Attachment (i.e. valve/trigger). I have seen some problems with brand new Bach 42 leadpipes (where the mouthpiece goes in). I think this is due to consistency problems at the factory. If you get a new 42, make sure the mouthpiece fits correctly or you purchase a warranty.
Conn 88H - this make/model has been a standard for trombones since the 1960's and is still a wonderful instrument. There are many options (similar to the Bach) so you may find a Conn 88HT, 88HCL, 88HG, 88H-SGX, etc. All models are good horns just with different features.
Courtois Legend AC420 - this is a newer horn I've been watching for a few years. I tried a good deal of the different models and have consistently been impressed with every aspect of the horns. These are wonderful instruments and the price is comparable to the Bach/Conn/Yamahas of the world, but you get a much nicer case. Again watch the letters after the model number, my favorite was the AC420BR.
Yamaha 8820 or 882GO or 882OR - Top of the line Yamaha Xeno model (G is for a gold brass bell vs. yellow brass, R is different shaped crooks). These are well made and highly recommended. A blend of features from the Bach 42 and Conn 88 with the added benefit that Yamaha instruments are usually very consistent coming from the factory (no lemons).
Getzen Eterna 1047F - A quality instrument from Getzen. It is my understanding that these horns are made in the same factory as the Edwards Custom Trombones. Getzens are similar to the stock version of Edwards: lots of the benefits, but none of the customization.
Getzen 4147IB - Top of the line instrument from Getzen.
Yamaha Allegro, 448G and 620 - all are similar instruments. Even though the 448 and the "Allegro" are listed as 'intermediate' I think they are fine playing horns.
As I'm sure many of you will find with a quick internet search these are the more expensive instruments, and there are some really shiny ones that look great for much less. There's a reason those other horns are cheap. They simply don't hold up. The metal is often extremely thin in all the wrong places, and the solder joints are so weak that when a repair tech fixes something another joint will break. You'll end up paying someone to re-connect the entire instrument. Some even come with a one or two year warranty; that is a false sense of security, quality instruments should last 50+ years with care and maintenance. It is often cheaper for these manufacturers to simply replace the instrument than repair it (and still make a profit off your initial purchase!!!). So if you find something that is brand new and ridiculously cheap, I suggest you look away immediately.