When I built the back-garden gate where we last lived I wasn't much into woodwork. I had:
. handheld corded circular saw
. try-square
. roll-up steel rule
. 1-metre rigid aluminium rule/light sabre (put the bloody thing down, Fred!)
. Sandvik hybrid cross/rip handsaw (didn't do either very well)
. tenon saw
. mortise gauge
. orbital sander
. belt sander
. a few blunt chisels I didn't know how to sharpen
. a few screwdrivers
. a few clamps
. electric drill.
. a couple of light wooden trestles
Important point: if you build your own, don't omit a diagonal brace from the bottom hinge-side to top latch-side. The professional who charged us 1000€ for new main gates 15 years ago said the sheets of ash he'd covered the backs with were enough, but with time and weather they split and the things sagged. One of these days I'm going to jack them up and put in diagonals. It's quite a big job so I'm waiting for dry weather when I'm not cycling and we don't need to get the car out - maybe in 2023.
Hinges: I used two-part pintle-type hinges because they're a hell of a lot easier to mount than "normal" hinges, and you can lift the gate off for repainting. If you want to stop some evil-doer removing it you can drive a round-headed or cheese-headed screw into the post just above one hinge, so that it can only be unscrewed with the gate open.