Welcome to the forums!
You are right about TRS-80 Model IIIs. I've been looking for one for years! Does any other user on this forum own one?? (apart from Philip Avery). They seem as rare as hen's teeth!.
Have you taken delivery of that Amiga 500 yet?
Regarding technical knowledge, I had absolutely none when I started my collection in 2007. It's still sketchy in parts. I didn't start out to get into the innards of micros. My initial interest was just to have some nostaligic/historical computers I could display and give talks about when I retired in aboiut 13 years. I found that I was FORCED to learn a lot of stuff just to keep the things working (nothing is a pitiful as a dead computer). Over time as I learnt more, I found gaining some technical knowledge satisfying. I still get stumped by a lot of problems, but if one of my micros isn't working it just annoys the hell out of me!
What I'm saying is don't be afraid to dabble a bit under the hood..especially if you've got nothing to lose anyway. Knowing how they tick at the hardware level adds a new dimension to the hobby. There is a lot of knowledge out there and I've found most people are quite happy to share it.