You’re right, Uniflex is neither a big footprint nor a high-demand user of resources. Most of the “work” is offloaded to the chamber and console interface boards. I don’t know what the Fluidsynth requirements are, but I can try to find out for you. Fluidsynth would drive the decision on computer hardware.
Yes, you can mix pipe and “external” sounds. Uniflex has great MIDI handling, so you can use external MIDI voices or products like Hauptwerk, and Fluidsynth is directly supported.
Dick Wilcox is fond of the Hewlett-Packard all-in-one touch-screen models, and they’ve been very satisfactory. I’ve only used one of those on two installations which run Hauptwerk along with Uniflex, and they’ve performed just fine. The key is the memory requirements of Hauptwerk – or, in your case, Fluidsynth.
I always recommend sticking to major-brand factory-built computers – Dell, HP, etc. – rather than something you put together yourself. I think it’s worth doing it that way for a number of reasons. Of course, if whoever is “feet on the ground” with regard to ongoing support is comfortable with a homebuilt, that’s probably fine too.
My recommendation is that you outfit the computer with a solid-state drive, which doesn’t have to be huge. Figure in the amount required for your Fluidsynth instance, then double the result and you’ll be in great shape. I’d also add an external “traditional” drive for backup purposes. RAM requirements would be dictated by the Fluidsynth system.