I'm probably not a big enough geek to help you out alot but a few important tips to upgrading or w/e you plan to do is have a budget. If you could tell me maybe what games you would be playing, that would also help.
The mobo (motherboard) you have now may be sufficient enough to play the games you want, but if you want to play any 3D games you will have to invest in a new video card, high end video cards can be cashy, and more often than not you can't even utilize all the power you are getting because (yet again coming back to the mobo) your mobo might not communicate well with your video card, if it does at all.
Judging by what you have listed thoses comps prolly cant handle any high end anything (no offenses intended). Sorry to say your out of luck as far as the amd comp goes i really dont know alot about amd (i am an intel kinda guy). Someone else will prolly have to help you with that.
Im assuming since you want to upgrade these you know something about how to put computers together, and what (if any) setting you have to configure for new components to work.
I honestly think that your best bet (for the intel one that is) is to try to find the exact make and model of its mobo. Once you have this info, you can determine what your upgrade options are, as far as proccesor, RAM, Vid Card, etc.
Another problem you may run into is the fact that your comps are not powerful enough to run Windows XP well. I'm not sayin you can't. Well, Actually I am 16mb of RAM is simply not enough.
My biggest problem will have to be your RAM you really can't run much with 16 and the Celeron kinda hurts, but like you said you want to upgrade. Get back to me on the exact specs of the Intel Machine and I'll try to help you out
Sorry in advance if you already knew all this and I just completely wasted your time. Your post made it sound like you didn't alot about this so, like i said, sorry if i offended you.
Hope this helps