You don't want an integrated video card for games. "Integrated" means you don't really have a video card, only a chipset built into the motherboard. They tend to be very low end, which would lead to "sticky cursor" and always having to reduce the effects in the game options menu to get them playable.
I don't know which "old games" you have, but there will probably be some of them which will not work in Windows 7 or Vista without tweaking. Check the
***Windows 7 and Games*** thread for which games have worked with Windows 7. The problem isn't always Windows either. Sometimes dual and multi-processors can cause problems, depending on the game.
If you want XP, you may want to consider buying from a place that custom builds computers. You may find some place local to you, or you might check what this site has
http://www.ecollegepc.com/They still offer computers with XP and their prices are reasonable. Also they have a good record at
***Resellerratings***.
If you need help putting together a configuration for adventure games, let us know what your budget is.