A 32 bit OS has a limitation of 3.5 gigs where a 64 bit OS right now can do up to 128 gigs of memory.
32 bit versus 64 bit on a video card is how well the graphics show up. the more bits you get the better the graphics and the higher the resolution.
I nor anyone on any site would be a fool to guarantee the game will run without lag. I have seen gamers spend thousands on a system to be mad because it does not give the FPS it says by 5 or 6 frames.
I'm telling you the specs as long as long you are better then the minimum the game should play.
Another thing to understand is even if you built a brand new system today in less then months it would be out of date. Nobody is going to guarantee what you are asking but only suggest you get your system above the minimum requirements and then you can play the game.
I spent 1800 on my new system less then 2 years ago and the month after I bought everything there was a newer video card that came out with more memory and faster graphics.
Either upgrade the video card and the system memory or consider building a new system or buying a branded system. The budget of a better system complete can be between 550 and 1500 depending on everything you want.