Where to start - maintenance on a 340

Removing the delay box is pretty straightforward. The ignition box will be a little harder depending on what distributor it’s running. If you want to remove it you may have to convert back to a factory type electronic ignition or points setup. If the ignition box is working I’d leave it alone. Oh and 10 years isn’t really that long. I wouldn't pull it all apart just yet. Get it running, tune it up and it could be just fine as far as leaks go.
I guess I should have added that there is a bit of oil in the coolant and some oil leaking from one head.

My plan was to drain oil and coolant, pull the oil pan, flush the coolant. Then change all gaskets and filters to see if that fixes everything.