single player should play with some high settings down to some low... so medium ish..
with pc gamning its best to find what works best on a per card basis. so you will often go through the first level tweaking settings as you play.
so start with medium and you want to aim for a consistent 60 fps.
some people go for a minimum of 60 fps while others go for an average. to get a 60 fps minimum you will have to play at lower settings . average will allow more eye candy but you will also have to put up with potentially less smooth gameplay and screen tearing...
On my laptop, (4GB ram, 1GB dedicated graphics ATI HD 5650, 2.1GHZ triple core processor, running at 1600x900)
the game runs slow on everything very high, no AA. (used to get 17 fps but now I get about 7-10 fps...it might be the dust in my fan making high temperatures but I'm not sure.)
So judging by that, I'd say you'd have no problem running Crysis 1.
it depends on the resolution if you'll get good frame rates.
If you're hesitant on getting Crysis, first consider that it's a great game!
Maximum edition cost me £7 British pounds and was well worth it as it contained Crysis 1 and Crysis Warhead. (Crysis Warhead contains the multiplayer game called Crysis Wars.)
Secondly, you can always just try the Crysis 1 demo to see what kind of frame rates you get.
On a smaller resolution (1280x900 to 1600x900) you could probably run everything maxed out with AA off. (AA doesn't make much of a visual difference especially the kind Crysis have incorporated, it's apparently a buggy sort of AA. There might be some configs out there that create better AA systems)
On a resolution of 1980x1080, you could probably get a decent frame rate at max with no AA but on High and Medium no problem.
It depends on the resolution and how many fps you want.
30 fps I'm sure you could easily reach but 60 fps, perhaps.
If all else fails (you can't download the demo?? Don't have your PC built yet??)
then look on YouTube Crysis max settings gameplay with whatever specs you want to check out. You have quite a good system, much better than my laptop of course.
if you look at my system in my sig. it runs crysis at 30 fps minimum maxed out x2-x4 fsaa.
your cpu is comparable to mine when i disable hyper-threading. and dont run it oc'd
your gfx is a couple of steps below mine... even though yours is a higher number...
the second hd x6xx means it is lower spec and because amd changed the naming convention even cards with higher numbers like the 6870 get beat by my 5870.
seems my card comes in just under or between the 6950 and 6970 depending on the benches used.
It should be playable on medium settings. Yet, crysis is already 5 year old game, and there are certainly games with better graphics. I think best graphics belong to Witcher 2, while the second place is taken by Battlefield 3.