Let me tell you right now, as a fellow Rift player, you're going to need some serious horsepower if you want to play that game on its HQ settings. I had a Phenom II 940 and a Radeon HD 5870 and I was still having to set some settings lower.
If I were you, and you're starting out, and money isn't a serious problem (within reason of course) then I'd suggest going this route, I'll save linking exact parts for now, this is just a few ideas.
Get a minimum of a high speed quad core. Intel i5's are fine, AMD Phenom II X4's are also ok. At high resolutions, the CPU won't matter as much as your GPU anyway
4GB is plenty, 8GB would be slightly overkill for Rift, it barely uses more than 4 GB on my setup with 8GB. The price is right however, so 8GB would be fine
A fast SSD would be nice, but more realistically, a 1TB 7200 RPM Hard drive from Western Digital or Samsung would be fine
A minimum of a Corsair or Seasonic 600 watt would be best
My favorite right now is Gigabyte, but a lot of folks trust Asus and ASRock (also Asus) right now too.
Doesn't really matter, but it's good to have for other things
This is where you have to decide what your primary focus is and what your budget is. If you can afford it, get a Radeon HD 6870 or higher, or a GeForce GTX 570 or higher. If money is a concern, the lower Radeon HD 6850 will still play the game fine, as will the GeForce GTX 460/470/480.
I wouldn't recommend CrossFire or SLI unless you're running a 24" monitor or larger with a minimum resolution of 1920x1200.
Onboard would be fine, but if you want to free up some CPU Cycles, get a Creative X-Fi or one of the offshoot brands of the X-Fi (Auzentech).
For reference, my system is currently:
AMD Phenom II X6 1100T
8GB Mushkin DDR3
2 x Radeon HD 5870 in CrossFire (performance gains are limited right now since they're still fine tuning the engine, but I CAN turn up a few more settings with the second card now)
The rest of the parts don't matter too much.
Oh, and I'm on Faeblight Defiant side.