MadeWillis - 2:23 pm on May 21, 2010 (gmt 0)
Correct me if I am wrong, but I think the OP is considering starting a program for his store, not put affilaite links on his site.
The downside to affiliate programs is that you risk losing natural inbound links. Affiliate links via 3rd party networks will all typically redirect through their servers which negate the link juice. This can also be a good thing if you let your program run on auto pilot, since you won't be monitoring who is linking to you. Too many links from one site or from a bad neighborhood could harm you, so this actually helps you.
If you will run your program with tight management and limited affiliates consider starting your own program. You could get some SEO benefit from that. We can't really recommend specific networks on this forum. Do a few searches and you should get a pretty good idea of who the larger networks are.