Not cheap. I just spent 7 months completely redoing my garage - almost exactly like what you are talking about.. from nothing and a buried wire from house for electrical to insulated, new electrical (including new subpanel and ug run to main in house), finished, added a window and replaced another, new door, some paint..etc. I did it all myself with exception of running ug feed which an electrician friend helped with (more I helped him a little). Added thermostat and electric heaters.
It’s run around $7k somehow. Thats with concrete floors (gonna stain them eventually). Permits will run you an extra $500-$1000 probably. If you need a subpanel in garage (and you probably will if you want multiple circuits) your main would have to have room for the breakers and capacity for it.
I got a quote initially on only upgrading the electrical and a new main in house at around $6k alone.
$20k — yep that’s probably realistic if you hire out and need to UG a new electric feed. maybe more like $25k in the end since these things always tend to go over budget. The thing is — with your temp swings you’re gonna pay a bunch of extra $$$ to keep that climate controlled allthe time to boot. Don’t know how realistic it really is unless you gotta lotta cash to blow.