RAID is a way to have disks work together, mainly to offer some safety for your data. (by either mirroring or parity)
The techkids here commonly use it for performance though, which RAID0 represents. (technically it isn't RAID though, due to the lack of redundancy)
RAID0 basically splits (stripes) data so 2 disks are used at once, think of writing a 1GB file, half gets written to one drive half to another which results in double the performance. Of course this is oversimplified but that's what it does. Of course if 1 drive crashes you lose all data since you miss half the file.
RAID1 mirrors all data, it writes the same data to both drives, ie if a drive fails the other takes over.
RAID2 is not used, it requires tons of drives and does some ECC stuff which is built into drives nowadays.
RAID3,4 and 5 basically use a drive for parity, the difference is doing it at bitlevel or not and whether to use 1 disk for parity or putting it on all drives. Exact differences aren't relevant since your cheap controller won't support 3 or 4 and RAID5 is more common anyway.
RAID6 is RAID5 with 2 parity disks, you can't afford a controller that does that nor is such a thing useful for you. (it's really rare that 2 drives in an array fail at once, if they do it's caused by something that took down the whole system anyway (power surge or whatever) in which all drives are screwed anyway.
RAID7 is used by a single company, not sure what it does nor which company it was, again you can't afford nor need it anyway.
There are also some ways to combine multiple RAID levels, ie creating an array of 2 or more other arrays, these are 10, 01, 50 etc. They require more drives as well.
Can your drives work in RAID? Yes they can, it's not recommended though. You should use identical drives for best performance.