my 1st 340....yea

I have built a number of 340's for my Formula S. I raced the original for years with no issues turning a best of 13.48@105.38 at OCIR. I collected 2 other 340's when they were cheap and kept them for spares in case I broke the original. Never happened. had over 350 runs on the original engine.
My recommendations are to do the minimal machining necessary to restore the block and heads. Both my rebuilds were +0.020" which was an available O/S piston in the 1980's. Not sure they are now, but this allows you to go to +0.030 in the future. A +0.020" 340 is a +0.060" 360. But deck height is different.
Try to keep the highest compression ration possible without milling heads. 10.25:1 was stock. If you mill the heads, make sure the intake faces are also milled to assure proper manifold alignment.
Keep the cam in the 284/484 or lower range for good street manners.
Check the vibration damper for TDC and use timing tape or a degreed damper to make sure you have accurate total advance timing.
Recurve the distributor for 11° Distributor advance (22° crankshaft advance) so you can run about 12° initial advance. This gives great starting and idle characteristics. My 340 starts in half a crank most of the time.
Run an aluminum intake for weight reduction.
Headers are not really that important on this type of engine, but stock manifolds are expensive if you don't have them.
Clean up the ports at the inlet and bowl areas as best you can. Lots of casting and machining flaws here that hurt flow. Have a 3-5 angle valve job done for better low lift flow. Run an AVS2 for good street manners if you don't have the original AVS.
I have heads, distributor and valve covers if needed.
Stock cooling should work but run a viscous drive 5 blade radiator fan and shroud. A higher volume water pump would be good if you can get one, otherwise stock is fine.
Be careful with the bypass hose if you use the 3/4" factory one as they can burst under pressure (read high RPM). Had this happen at OCIR once and warped the head a little. Silicone hoses would be best if you can get them. Otherwise convert to the 1" hose which is stock for all 1970+ engines.

Best of luck with the 340. They are fun to drive and rev to 6500 real nicely and sound delicious doing it.