When we were shopping for a PC for my girlfriend, who likes to play some games on occasions, we found out that most PC come with ****** on board graphics that won't be enough to satisfy lag free gaming that most people want. So either prepare to shell out some money for something "decent", or build a computer up to your spec that will chew through every game, or anything else for that matter. We ended up buying an average computer and later I swapped out the PSU and a graphics card.
Just as another example. Few years ago a board member here assembled a computer for me. We started with just the basic stuff, because I didn't have much money to spend and wasn't really interested in games. Later when I wanted some performance out of it, I just made some modifications to it, think of it as very expensive legos, later on when you need more you can buy a better part and improve the performance of your machine and be happy with it. As it stands today, the only original parts are; mobo and the hard drive
But I have not had any problems playing any game I want.