Would I be able to run XP (or, for that matter, WIN 98SE) based programs in Linux? Are there windows emulators which will permit that, or am I going to need more horsepower than the single core 1,7 Ghz processors with 2GB of RAM (Maxed out)?
Horsepower should not be an issue (if the programs could run on that machine under XP).
Getting the programs to run using a program called wine on Linux? Maybe. I really don't know. It worked for the program I wanted to run (Starcraft). If you're looking at saving $12K I'd think it's worth an afternoon trying. Of course if it breaks down the road you've got no real support, but I suppose you don't with XP either.
If that doesn't work, you could run Linux as your OS and use KVM and install XP as a virtual machine (with your data files on a seperate virtual drive in case you need to reinstall XP). Then, perhaps, you make a copy of the VM just after you get it all set up and running so you can simply "set the date back" every few weeks. [Note: I do not know or care anything about MS software licensing. I said you could, I didn't say you should].
There may be solutions from VMware (Workstation) or MS (HyperV) that would allow you to avoid Linux completely. Performance will probably be better with a Linux OS and XP VM (vs using a MS OS), but then you need to learn at least a little Linux.
BTW, while looking something up related to this response, I came onto something called Virtualbox. Might be worth looking into.
Now, one more time, "if it breaks down the road you've got no real support".