If you want to use a hardware raid controller you really need to stick to their recommendations on hard drives or the family of supported drives. Unexpected problems and lack of support could come back to bite you. 3ware wouldn't even talk to me the first time I called them when I had issues with a server using Seagate AS drives on a 9650se.
If you can't afford the right drives in the size you want, maybe you could scale back to used 1-1.5TB enterprise like the WD1002FBYS or similar. I have 6 of those, all purchased used from eBay for $65-75 used after verifying they had a warranty. 4 are in my 8 disk raid6, 2 for cold spares / occasional backups. The other 4 drives are WD1001FALS, older models that could enable TLER. I didn't plan on hardware raid when I started buying the FALS drives initially, but once I started down that path and went hardware it ended up costing me more than if I had just bought the right drives to begin with. I eventually found a home for some of the other drives I stopped using or couldn't use.
For less expensive new drives you could consider OEM (WD/Seagate drives made for HP, IBM, etc). There's usually a bunch of eBay sellers with quantity, but those drives won't have a warranty from the drive manufacturer and I have no idea if the company they were made for would support you. It's risky.. Work picked up a batch of 20 Seagate ST31000340NS (1TB, same model, similar serial number, slightly different firmware) a while back for around $1250 I think, so far so good. Not a bad deal when you consider those drives sold for ~$150/ea. Unsure if there's anyone selling 2TB OEM enterprise.
I have no idea what your storage needs are, if a 6TB array like mine would cut it or not. 1TB drives are common and fairly inexpensive. If I had to do it again and could properly plan, I'd go with an 8 disk raid6 again at home. Although maybe I'd take another crack at software... I ran a software (Linux, md) 3 disk raid5 a few years back, perf wasn't so great and it was rough when rebuilding. 8 disks vs 3 should have significantly improved performance and maybe some additional tuning could improve the rough rebuilds.
If smaller size drives or used/OEM aren't going to work, maybe you could pick up a simple SATA HBA and do a software raid instead. I mostly use hardware at work, but a coworker does a decent amount of larger servers / storage (8-16 disks) with Solaris and ZFS. A 6 disk RAID-Z (like RAID5) I have access to has decent sequential writes at ~350MB/sec, similar to my array at home.