For fence building yes. A circular saw and a drill. For pavers you need a water cooled tile saw with a diamond blade but that is a borrow or rent item if you can. A wire tracer is nice. We rented one.
Lot of people saying battery powered stuff. I take opposite view. No battery stuff unless you need it. Problem they are more expensive and your always charging and replacing batteries. Just less sustainable. No gas stuff either same reason.
Yes. I am not sure I always notice the community too. Lot of the relies suggest that.
Mulcher, I have no experience. We take our leaves to the county site and let them take care of it. We did try to compost them for awhile but just too many.
jigsaws (amzn link) are quite handy if you're messing around with plywood or thin sheet metal.
cordless drill, pretty standard. I like the ones that use the regular chuck but have the option to go into the rotary hammer mode.
multimeter. Kinda sorta technically a power tool lol. But kinda necessary if you do any electrical work. Or even just for checking car batteries or whatever.
I think every house should have a decent drill and air compressor. After that, vibrating multi-tools can handle most other jobs, just sacrificing speed and accuracy.
The only tool that I feel really revolutionizes your options in the yard is a quality power washer. Helps you restore junk to a perfectly usable state and makes things look amazing.
Also removes that slippery algae build up that can be a real Hazzard in the yard.
How's big your outdoor space? I've never lived anywhere I couldn't manage with a non-motored push mower, even with my energy impairment disabilities, and much prefer them. Takes much less space to store too and of course it's infinitely more sustainable.
Is there a frequent chore you find particularly irksome? There's probably a non-motored tool or technique to make it easier. IMO those are the things to buy and give storage space to. You'll likely get farther for the same investment.
It's been a long time but I'm sure we were able to mulch our leaves with the push mower once the blades had been properly sharpened. (Where I live now there's an unfortunate deficit of leaves (you could always try posting some of your excess to Scotland ;) and in between I was four floors up without a garden). A bit large if you don't otherwise need a mower though but going for a walk across the grass is some of the easier garden work.
I've seen videos of people making contraptions involving things like rotary saw blades and hand cranks but that's way far beyond me. I do like watching clever gardening videos though, especially in January when it feels like winter will never end.