Hold off on the lapping. Shoot the rifle for a while and see how satisfied you are with it before spending extra cash. There is not that much to gain from lapping a factory barrel except that it MAY improve accuracy a tiny amount, and it will make the barrel easier to clean.
Good choice for your first centerfire rifle. Spend the rest of the budget on a scope and ammo, and sometime in the future look into a trigger job. Good hunting!