Someone should be able to confirm the age of this outboard soon. Once you have year of manufacture - you can search specifically.
This is a similar thread: https://www.rib.net/forum/f36/identi...eto-47234.html
A better shot of the manufacturer plate would help.
You should definitely check the thermostat, yes. If you remove the housing - then have a gasket available. You don't necessarily need to replace the thermostat, depends on the condition, but a wire brush (using soft brass bristle brush helps), and you can test in boiling water. Sometimes there's a sacrificial anode in the thermostat housing too, well there is on Tohatsu engines. Don't over-torque the bolts on refitting, tighten, then nip up.
Check the other sacrificial anodes too, and replace where necessary. Needed to be fitted dry, no grease on them. Also grease all nipple points. A spray of white grease on any linkage points wouldn't go a miss either.
Electric wise - check bullet connectors, and any corrosion on terminals then lightly sand and reconnect. Manufacturers didn't use tinned cable - so not uncommon to have electrical gremlins.
If it's got power-trim - check the fluid level. Use ATF fluid. On Tohatsu - they recommend Mobil 220, but if you can get a workshop manual, that will confirm. Quicksilver manufacture too.
On the lower unit - then replace the fibre washers on the fill and drain screws. No point going to the expense of a service to let water ingress due to these weak points. Depending on the condition of the water-pump - then renewing not just the impeller but all the gaskets and housing makes sense.
Compression - don't have specific compression, but I'd have thought in region of 110-120psi. The main thing is for the reading to be consistent across all cylinders. Pull the safety lanyard, and test individually.