Shoot the gun first
Lapping the lugs to get them to bear evenly (and equally) is something yo don't need to worry about, until you have done alot of other things to your rifle and still don't get acceptable accuracy. If done incorrectly, it can, as you know cause serious problems.
Lapping the lugs/trueing up the action is something best done when building the rifle, before final headspacing. It can be done after, but if not done carefully, can cause you to need to have a lot of more work done.
You got a new rifle. Shoot it! Shoot it with different brands of ammo, different bullet weights. If you are into handloading, work up loads for it. Find out just how well the rifle (and you) can perform before you start tinkering with the gun. You just might find out that you don't need to!
Some folks will buy a new rifle, and then nearly completely rebuild it, (beacuse they like to), while others will spend time and money "improving" their rifle needlessly, simply because they didn't bother to find out what it was really capable of first.
Go out and shoot it a bunch, find out what it likes, and doesn't like. And then, if it isn't performing as well as you want, come back with details and we can suggest ways to go. Most rifles will out shoot most shooters, and spending money and effort for "improvements" that you cannot take advantage of is useless. I've seen people spend alot on "improvements" to get a rifle that will shoot 1/2 MOA or better, when the best they can shoot is twice that! Hearing them whine about how much they spent or how much work they had to do, and still the rifle will only shoot "xx" groups! Then when someone who can really shoot shows them what their rifle is capable of, you should see their faces!
Some people are naturaly fine shots. Most of the rest of us have to work at it, and some never get there. If you aren't there yet, you won't get much benefit from improving your rifle.
All else being equal (and it almost never is) bigger bullets tend to work better.