You can buy a 1TB drive for $5 more (on newegg or your other online store of choice), so I'd seriously consider that, or a 1.5TB drive (which has roughly the same price/capacity) if you could use the space. 2TB is new tech and too expensive for now.
Personally, I've had Seagate and Hitachi Drives lately, and never had a problem. Years ago, I had a Western Digital as well, which I didn't have a problem with either. With hard drives, it's kind of a luck-of-the-draw deal, so you can get a lemon with any brand if you're unlucky... I wouldn't worry about the brand overly much.
As far as good software to copy stuff over, I personally wouldn't think you need any. You can just connect the 2nd hard drive, format it, make sure it behaves 100% right out of the box - no bad sectors, no weird noises, no slowdowns etc.
Then, you can burn this CD with imgburn and use the "HDClone" tool which comes on it (untested, but heck - worst comes the worst you'll just have to format your new drive again if anything doesn't work right):
http://www.ultimatebootcd.com/
Alternatively, you can boot from a CD like this:
http://www.ubcd4win.com/
(this one is a bit harder to build but just follow the instructions - it requires a windows xp installation CD for copyright purposes)
And then the latter boots you into a cd-bootable windows XP environment where you can simply use windows explorer to copy everything over to your new hard drive and then all you need to do is just install/fix the bootloader on your new disk using these steps:
1. Boot up with your Windows XP disc.
2. Select the option Recovery Console.
3. At the prompt, type "fdisk /mbr" (without the quotes of course)
4. Restart your computer.
Personally, I'd download UBCD and try HDClone first, because it seems like it'd be the easiest (and completely free) solution to your problem.
Hope it works out.
P.S. I assume you're using XP. If you're using Vista, the bootloader fix might be different, so look it up "how to fix vista bootloader" or "how to restore vista bootloader" or whatnot...