Very first mod should be getting rid of that "balsa" wood stock........that is the easiest one to do........
My "must" do M14 list is as follows:
-clean all the packing grease off/out of rifle
-properly lube rifle and check for smooth function when racking the action. There should be no binding and the bolt lugs should fully lock.
-check gas cylinder play and barrel indexing. Every Nork M14 I have ever seen needed some work shimming the gas cylinder......3/4s of them needed the barrel re-indexed so that barrel sits square in the action.A mis-indexed/aligned barrel can cause the oprod to bind and not move smoothly.
-Swap in a National Match oprod guide and USGI oprod spring. Easy and pretty cheap.
-I like to run a Smith Enterprises type gas lock front site.....the rear sight I leave on.......the only mod I do is drill the aperture larger and have "Ghost Ring" style open sights.
-Then I install A Smith DC Vortex Flash Suppressor and a over sized bolt release...........
-If the bolt headspaced is out too much, then I will swap in a USGI bolt......(preferably a nice TRW bolt.....

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For the average guy, I would just worry about the stock, gas system, oprod guide & spring. These 4 things will tighten up your groups quite a bit.........