Richard, you really can't do significant amounts of upgrades to a machine that "old." For example, new motherboards are now ATX, not AT, and wouldn't even fit into that AT case. You'd need a new, ATX power supply as well. The only things you might be able to use from that machine would be the floppy drive, CD-ROM, modem, and sound card. In other words, you'd be building a new computer and then adding those few, relatively inexpensive, legacy components. It won't be worth it. If your computer isn't brand new, I'd recommend you hand it down to your son and get yourself a new computer.
You'll probably have problems trying to burn to a CD over the network. Network speeds, even 100Mb Ethernet, aren't fast enough to keep up with a CD burner. If the CD burner can't get the data when it needs it, it could ruin the CD. You'll probably have to copy the files over the network to the machine with the burner and do it off of the local hard drive.