For an art computer you shouldn't need to spend over $1500.
A Velocity Mirco system would get you some great options for your money. Alienware would get you some terrible options for your money. You also may want to check out any Origin or Falcon Northwest PCs if you're looking for that "gaming-esque" style. If you want to go more mainstream Dell's XPS line is ok, but not great. If you really want the best options though for a performance machine the best choice is usually to build your own. You said you weren't comfortable, but it's really not hard at all. Especially if you can get a bundle deal where you don't have to worry about finding compatible parts.
If I may ask though, what exactly happened to your old computer? They don't just "die" usually a component fails.
This is a hard one to ask, especially if your on a budget.
But if your looking for something cheap the new google laptop looks good. ( not 100% sure if its good for art).
If you don't care about the price and want one that will last a life time I'd say get a big sturdy Toshiba laptop ( there quite expensive but you won't regret it, there great laptops. I've got one myself and it's been around for forty years! Not that I'm forty! It used to be my dads for a little while, and it's worth £1800! But we got it for 1200!)
I've got photoshop and illustrator and that's £1000 pounds of software and the Toshiba laptop I have is very strong, reliable, long battery life, GREAT for art and MUCH more!!!!!
Head over to here [link] and configure a system along the following:
Case: Any would do, I'd suggest a full tower, like the NZXT Phantom. Power supply: Silverstone Element ST65EF 650w Motherboard: ASUS P8Z77-VPro CPU: i7-3770 Cooler: CM Hyper 212 RAM: Crucial Ballistix Sport 16Gb (2*8GB) 1600MHz GPU: ASUS 660Ti-DC20 1st hdd: Samsung 256Gb 840Pro ssd (OS and programs) 2nd hdd: 3tb Barracuda (Storage) OS: Windows Pro or Ultimate 64bit (Windows 7 or Windows 8 whichever you prefer)
Total: About $1900.
As for a monitor you could go with the Dell U2713HM for about $700.