Trombone

School Hire

If your school offers an option to hire a trombone, I'd recommend that for the first year.
Trombone slides are delicate and can be tricky to protect and handle to begin with.
Also, some students begin on trombone and discover throughout their first year they may be more suited to Euphonium, Trumpet or Tuba.

Given that a good new trombone is worth almost $1,000, and most schools will hire you one for $200 - $250 for the year, this seams to me to be a good option. If your child is thriving on their trombone and loving it, then I'd definitely recommend you buy one at that point.

Yamaha YSL 154

(recommended)

Current Street Price with an Educational Discount:$ 1,095
Yamaha's student trombone, the YSL 154 has good tone and projection.
It is well built and the slide last very well so long as it is maintained well.
 

Yamaha YSL 456

(Highly Recommended)

Current Street Price with an Educational Discount:$ 1,995
The YSL 456 is Yamaha's Bb/F Intermediate Trombone.
These are a significant step up from the YSL 154.
They can often be bought second hand in excellent condition for $1,250.
This trombone will last a student right through High School and beyond. It is used by many amateur and professional players, especially those who might play another instrument such as Trumpet, Euphonium or Tuba and need a really great instrument on a budget. 
(This is the Trombone I personally own and play)

SECOND HAND

Please read my guide to buying second hand.
Fully serviced and from a reputable second hand source, in great condition, you can expect to pay around:

Yamaha  YSL-154 $ 670
Yamaha YSL-354 $ 750 (intermediate level - no Bb/F trigger - a good upgrade)
Yamaha YSL-456 $ 1,250 (see above - highly recommended for high school and good primary school players)