Good wheels can move to a different bike, even if they need respacing. Sealed bearing hubs are a better option for your uses. A wider rim is also good, 23mm or so. WTB chriscross would be aces, tuff, straight, tubelessable. Formula hubs are good value too. But there’s nothing wrong with used wheels as long as the brake track isn’t worn out and the bearings/threads are good, and they’re a lot cheaper than new / handbuilt.
Good cranks likewise, pick your BCD to suit your gearing requirements, 144 is cool for the street but will limit you for SSCXing with a 42T min and need $$$ freewheels. stay away from vintage cranks, they can crack if you don’t know what to look for, the sugino messenger / rd2 is a fine cheap option.
Basic cartridge BBs, cheap and bombproof, UN55, don’t bother with other stuff unless you’re throwing money at an SKF, used only if you get one free/with cranks or already have one. they’re cheap.
Brakes/levers: drops or flat bars? Forget stuffing around with cantis for this setup. Used is fine if they’re not bent/busted/rusted.
Drops: mini vees in 85mm arm length, tektro RX5 plus adjustable noodle and better pads.
Flatbars: BMX/MTB regular vees plus Shimano levers (eg BL-4600 / BL-T780 / BL-R780 all do caliper or linear pull), or some Avid speedials.
Chain: eh, a $1 BMX chain from clickbike.com.au is hard to beat right now. Sure an Izumi is nice, but…
Cables/housing: new, not worth skimping on something so cheap. linear housing if you want to improve feel.