I'd also recommend the 360 for you, especially since you are interested in online play, and having it as a console for your kids. The 360 has a massive library of games out there, plenty of which can be purchased used very inexpensively.

The PS3 is a nifty machine, but for what you are wanting to use it for, I really think the Xbox 360 is your best bet. And reading through the other posts, it doesn't sound like I am alone in that. Though make sure you buy it new, not used. The older models had a tendency to melt themselves from over heating. The newer models have fixed this problem. With a new console you wont have to worry about the over heating (the infamous red ring of death that you have probably heard about), and you'll have the piece of mind of a decent warranty.

Alternatively, if you were not very interested in online play, and mostly just wanted something to keep the kids busy, and if they are not old enough to feel shafted by getting a last gen console, the PS2 is absolutely fantastic, and has a massive library of really good games that can now be bought really cheap.