Let me give you a little info.
JTAG (… Group) - Method doesn't work online (hasn't for years), good for playing offline and cheaper.
RGH (Reset Glitch Hack) - Can be used online, more expensive.
RGH is the better option. It is recommended that if you don't have any experience with it that you just buy one instead of doing it yourself, it may be too much work/too complicated.
You usually want one with "Fast Boot" which will boot instantly and not take minutes to boot. The newer model ones are better.
After getting a RGH Xbox 360 you will need a stealth service to prevent you from getting banned instantly when going online, you will need to by a new KV (Key Vault aka Console ID) after you get console banned (usually every 1 to 2 weeks or something) about $5-$20 I think. (That is why people make modded accounts to make back money).
People mostly go with PS3 because its easier and cheaper but xbox 360 modding is a little rarer.
Yes, you can get games for free by downloading and using a hard drive to copy & run them.
You can spoof your account to have xbox live gold and apparently I think you can spoof Microsoft Currency... no 100% sure on that one.