I agree that the biggest question may be how many of your kids may be visiting you at once, including their own kids. That determines how much space you need. Other than that, get the smallest place you can tolerate because if you eventually live with another woman, you'll probably need to get a new place anyway.
If they aren't visiting a ton, it may be cheaper to put them up in hotels than to buy a bigger place.
I'm not sure how old you are, but also consider that your mobility and strength is going to decline. At some point, you'll need to be in a condo or apartment so this may be a time to make that jump.
My wife and I are going with a 3-bed, 1700 SF ranch. I enjoy shovelng and mowing for now. We have 5 kids between us, but they may all end up living fairly far away (all around college age right now) so we want to have a little extra space but not waste it either.