Ok. I'm sure this thread has pretty much been answered to death, but it's late so I'm just going to answer it again. I didn't really read any of the other replies so forgive me if I'm covering something thats already been said. If you don't know much about building your own PC, find someone you trust that does. This is a lot of money to spend on a first try. If you don't want to get into the innards and details of building your own, you could look at a Dell and basically, when ordering..just strip it down to just what it needs to run, then add what you want when you get it.
Anyway, $1200 is way more than you would need to put together a decent intel system for multimedia purposes. A good rule would be to keep it minimalistic. Don't add components you won't need. This saves IRQ's, money and time. This doesn't mean buy the cheapest things, but theres no sense in buying a DVD drive and decoder if this is for recording only...
First off, figure out what you want inside and what you'll need to power (HDD's, CD-R's, etc..) A good ATX case can be had for under $100 with a power supply large enough to handle an average number of devices.
Get a 3.5 floppy drive. You never know when you might need it. These are only a few dollars.
SDRAM and DDR RAM is cheap. Get a lot, it never hurts to have too much. Right now I'm running with 512MB.
The processor brand and speed are up to you and your budget. Personally, I think the AMD cpus are a better value and I dislike the P4 for various reasons. Right now I use a P3 550, but with current prices, I would suggest a 933MHz or faster.
Storage is also more of a personal preference. SCSI or IDE, it's up to you. IDE will be cheaper and easier to set up. Usin two drives is also a good idea. Keeping your system separate from your music data can save you a ton of trouble if your OS somehow becomes corrupt. You don't need a ton of space on the system drive, but nowadays, you don't see many IDE drives smaller than 10GB. You'll want a big data drive, 60GB are pretty cheap now.
As for video, it's really not too important for recording audio...a 32MB AGP card shouldn't be too much but get a good monitor. You''ll probably be staring at it for a long time and fuzzy and cheap monitors can be hard on the eyes.
Sound Blaster audio cards are well supported and high quality.
A note: Windows 98 is probably your best bet. Better support than 95, "lighter" in resources than ME, XP or 2k. (BTW, I hate Windows in general but I've found 98 to be the least annoying)
I'm not really up to date on hardware prices, as I haven't actually bought anything in a while. I think I remember seeing a guide for this on the Tascam website. Also, although you'll probably find cheaper prices online or in a catalog, buying your monitor and case at a store near you will save on shipping.
I'm tired. I'm going to bed. I'm probably forgetting some stuff. I hope this was somewhat coherent.