TROMBONE: With the trombone, it’s recommended to buy rather than rent. They are typically inexpensive ($75 - $100) but in one year of renting a trombone, you’ll have spent almost double than you would have spent just purchasing one. When looking into purchasing one, you should avoid “no-name” brands and go with standard instrument companies, such as C. G. Conn, Conn-Selmer, Bach, Yamaha, Getzen, King, Edwards, P-Bone and Shires. When renting or purchasing a trombone, any dents in the bell are easily fixed, while some in the crook of the tuning slide or hand slide may have minor effect on sound.
EUPHONIUM: Opposite of the trombone, renting a euphonium is going to much more cost-effective, as even used ones will run into the thousands. Some brands to look for are Conn, Yamaha, Schiller, Besson, Miraphone, Jupiter and Wilson. One big thing to look into with a euphonium is the brand, as well as if it includes a 4th compensating valve.
TUBA: Similar to the euphonium, renting a tuba is the best option, as you also have to figure out what size tuba your student would play. Brands to look for include Conn, Yamaha, Miraphone, Meini Weston, and B&S. One big thing to factor in for tubas is deciding if you want rotor valves or pistons. Both have their pros/cons, so it usually boils down to personal preference.