There are currently no webcams that will give you the advertised frame rate, even on a high end system. Webcams that are marketed as "720p/1080p 30fps" will give you 15fps at best, and these are Microsoft/Logitech webcams. One drawback is the included driver software. Logitech webcam software is junk, and the Microsoft equivalent isn't much better.
There are ways to achieve higher frame rates, but the procedure is beyond the scope of this reply, unfortunately. Suffice it to say that it requires complete uninstallation of the included drivers, and installation of alternative software and video codecs.
Whilst 1GB RAM is more than adequate to run webcam software, you are more limited by the fact that that isn't really sufficient RAM for most operating systems. I have 16GB in Windows 7 x64, and I'm thinking about doubling it. Processor speed and USB interface speed are by far the greatest limiting factors. An old PC will probably have USB 1.1, which isn't really fast enough for decent frame rates. Also, a slow processor will similarly hamper the transcoding of the video.
Another factor is the crap that's running in the background. This is likely to be a problem on machines that haven't had a clean down & reinstall for a few years. You'll probably find you have iTunes/Bonjour service running, Adobe updater, various intrusive bits of junk from Realmedia and Quicktime. And the real killer...NORTON! If you have ANY software installed from Norton (360, for example) your PC is probably being choked. For AV, all you need is Microsoft Security Essentials, and once a month, scan for spyware/trojans with Malwarebytes free edition.
Also remember, if you're trying to use a webcam at 720p/1080p, an older computer isn't really going to be able to handle the amount of data transmission across the Data Bus (imagine forcing a watermelon down a hosepipe).
And the biggest factor in all this...internet bandwidth. Upstream bandwidth at both ends will dictate data transmission, which will dictate frame rate, which will dictate how jerky the video appears. If they each have 880k upstream or greater they should be fine, but if they are using 2 tin cans and a long bit of string, forget smooth video. It doesn't matter if they have 100Mb downstream, each can only receive data at the same rate it's transmitted.