RAID 6 is probably overkill. How likely is it for 2 drives to die simultaneously? And if the array does die, how much of a problem is it going to be for you while you order in new drives and restore from backups? If it's just you, a day to restore would probably be acceptable - if this was a file server serving 50 people in an office - then a day to restore would not be acceptable, then RAID 6 would be an important consideration. Remember, RAID 5 has generally good reliability, the risk of hardware failure causing data loss in RAID 5 is considerably lower than human error, or malicious software.
In your case, it looks like you just want cheap storage of low-value data (I'm guessing publically available media) and a moderate cost if the data is lost - it would take a few days to rip the dvds, or install the games. So a lot depends on how you value your time. A 2TB RAID 0 array comprised of 320 GB drives would probably have a breakdown rate of about 1 in 15- 1 in 10 for each year. Is that acceptable? I'm guessing that it almost certainly isn't.
So RAID 5 is probably the only sensible option. If money is no object then a high-end 12 port SATA RAID card with hardware accelerator would be the best solution and leave room for expansion - The Areca/ Tekram card suggested by ArcaneDeath certainly looks like a respectable choice.
If you need a slightly lower budget, than an 8 Port card with hardware RAID5 and 8 320 GB drives will get you your 2 TB, but without any expansion space (unless you add another card), or swap out all the drives).
Budget around $1400 for the drives, and about $700 for an 8 port RAID card.
You can get bigger drives (e.g. 400 GB drives) but you will pay a significant premium for this - and you still won't be able to get a budget 4 port RAID card - as you will need 6 drives.
You also get reduced power consumption , heat production and noise, as well as leaving you additional expansion space on a single 8 port card.
If you aren't worried about the additional cost of the bigger drives (about $250) then I would definitely go for 400 GB over 320 GB. The price premium of 500 GB (another $500 on top of the 400GB) is probably too much for too little benefit over 400 GB.