You'll need to get really comfortable with wiring diagrams.
MK3 Supra wiring diagram for a 1989 (87-88 are very similar but different)
MK3 TEWD On-Line
Aristo wiring diagrams:
Basically, you'll keep the Aristo engine wiring from the engine components to the ECU, extending those wires to get the ECU in the stock-ish MK3 location, and tying power sources into the stock MK3 relay and fuse blocks in the engine bay and driver footwell.
You'll keep the 7M-GTE engine wiring harness and salvage the plugs for the body plug components accordingly and integrate that into power for all components and signal wiring to the dash, etc as needed.
I recommend getting a big sheet of pegboard, carefully mapping out all the components and plugs you need, establish the pinout for each plug, and only cut & reconnect one wire at a time. Buy some professional crimpers and the correct crimps & shrink wrap for them, it's much faster than solder and lasts much longer without issues.
You'll quickly learn why a quality wiring harness is a $1000+ issue, and worth it.