You need an Arduino, I'd reccomend the UNO, doesn't matter if it's SMD or the DIP version. You also need a USB cable for it unless you don't have one already.
You need a breadboard, some jumper wire and components to play with. For example LED's with resistors, potentiometers, push buttons, various sensors and so on. I don't know what you like to play with.
If you don't know what you want to do and which things you would like to play around with, just order one of these http://www.sparkfun.com/products/10339
. It matches your budget exactly.
I started with one of those.
It probably won't matter to you which version you get.
You can't replace the ATMega on you board if you buy the SMD version but I don't think that's necessary unless it breaks and they usually don't do that.
3. The kit from sparkfun is $100. You can get away with lower if you skip some of the components.
You can also check the parts list and buy the parts separately but I don't know how much that would save you. The experiments and the source code for the kit is available online at ardx.org
You can also buy a bootloaded ATMega328, a crystal and some caps plus FTDI interface and do everything on breadboards if you like. That's probably the cheapest way but you won't be up and running in five minutes like you are with the UNO.