What really sucked me into full-time PC gaming was Garry's Mod. Pick up CS Complete and Garry's Mod and play some of the online modes (Trouble in Terrorist Town, Zombie Survival, DarkRP).

Some good games to try if you haven't played anything on a PC before:

Crysis (series)

Starcraft (series)

Any Valve game (Counter-Strike, Left 4 Dead, Half-Life, Team-Fortress 2)

Planetside 2 just came out and it's a good representation of what's to come.

You can build a worthwhile PC for gaming today for under $500,, $1000 is way more than enough. Be sure to check if you have a Microcenter near you. Even if it's two hours away it's worth the drive for the prices.

If you don't want to build, just take your parts to an infotech (or similar) and give them $50 to build it. It's still way more economically effecient than buying a prebuilt from Alienware.

Inb4 Alienware X51 BS.

I have a non-ti 560 and run a 1280 x 1024 monitor. Only games I haven't maxed yet are GTA 4 and, to an extent, Just Cause 2. Still, high settings with 4x AA.

You don't need 16GB unless you are doing profesional video editing - and where is your HDD? 60GB will let you install windows, firefox, steam and... one game.

Drop the PSU to a 650w or 750w. Heck, a 550w is still plenty. Dump the savings on a better video card.

You can get a GTX 560 (non-ti) for around $140-$150 after MIR. Dat PhysX.

24" is as high as I would go at 1080p. 27" is too far. You should be A OK running any game at 1920 x 1080 all high settings. As for the HDMI question, it depends. Does your 670 have an HDMI port on the side? Does the monitor use HDMI? If not you could just buy an adapter for $5.

I went from a 99 Etower to a 2009 Athlon II x2 laptop. It had intergrated graphics, so it still sucked, but what a leap.

Definitely go Intel with $1000. Switch brands on case and RAM, and a Hyper 212+ will fit fine with any GPU. The real question is will it fit over the RAM heatsinks or is the motherboard arranged in a convinient manner?