It's highly unlikely that the modem will truly be provided for free from your ISP--most charge a monthly rental rate if they don't sell it to you. Assuming you're using cable, you just need a cable modem that supports the protocol your ISP is using, which is undoubtedly DOCSIS. The question is which version--some higher density areas that get higher speeds first might have 3.0, but 2.0 is what most use and will still be backwards-compatible.
Most modems will be DOCSIS 2.0 compatible, and you'll probably be good wit one. You'll just need to give your ISP the MAC address or whatever other information they request.
Or you can use the one they rent, and they'll do everything for you. In the long run, this is probably more expensive.
(DSL, of course, uses a different kind of modem, but you sound like you have cable.)