I was an employee of Rieman Music pretty recently (college side job), and I can tell you that within that particular area, your best bet is to actually purchase a student instrument outright, if you can afford it. As with most other payment plans, there is a (small) finance charge, which will add up over the course of 2-3 years of payments.
Perhaps the policies have changed within the past year, but while I was with the company, they have a "buy-back" feature, which means that say six months in, Johnny decides to quit the trombone, then you can return the horn and Rieman will give you back what you payed, less however many months of rent it would have been.
In other words, if you keep the instrument, you've saved yourself a hundred or two hundred bucks from finance charges, and if you return the instrument, you've spent the same amount of money. Of course, the issue is the up front cost. A trombone (if I'm remembering right) is around 7-800 bucks (brass instruments are generally more expensive than beginning woodwinds), and an alto sax is 11-1300 (most moving parts of any instrument, also made of brass). If you can afford to purchase the instrument outright, I would do that, AS LONG AS you have made sure the return policy is still in place. It really is the best financial deal you can get from Rieman.
Also if you purchase and own the instrument often that puts families in more of a feeling of possession/ownership and can incentivize the kid to stay in band!
Be careful of incredibly cheap instruments found online, they truly can be horrible and make the difficult process of learning music even harder. Generally brands like King, Conn, Jupiter, and Yamaha are great for brass, Selmer is great for saxes (at least beginning). If you can find a student model horn from one of those companies online for cheaper than Rieman, I would suggest doing that. However, often older, used instruments will need some maintenance. A chem/sonic clean for a brass instrument will run you around $100, and a complete repadding of a woodwind will cost somewhere in the neighborhood of $2-300.
As for appreciation of instruments, it really depends on the make and model. Older keyboards aren't worth much of anything, but an older, hand-made saxophone could be worth a considerable amount of money.
