Hello. I was wondering if it matters what RAM card you put in a computer, or if you can just stick any RAM card in a computer and it'll work.

There are varieties of RAM, and it does matter.
Sometimes the form factor keeps RAM from being physically installed, sometimes it is a timing issue that keeps the RAM from being recognized (especially in notebooks).
The easiest way to figure out what type a PC requires is to either go to a site like Crucial.com or Kingston.com and put in the mfg/model of the PC into their configuration tools or to find the mainboard number and put that in their tools.

Thanks, I just needed to be sure on that. About $53 I need to spend to get the compatible ones it says.

Yep, that works pretty well.

And one more thing, I have vista and I read I could plug a flash drive in and use it for RAM. If I did it, would it perform just as a RAM card would?

Vista will use it but RAM on a mainboard bus is faster than any type of memory using a USB interface.

And I have Vista 32-bit, what is the maximum amount of RAM I can put on it? It has 2 free slots out of 4 slots.

Depends on video card but around 4GB for 32 bit.

I have a ATI Radeon 2400 Pro.