There's a pretty good post over on
www.nationalmatch.us about how much accuracy you need in a rifle. As long as the rifle is more accurate than you can shoot it (offhand, sitting and prone), then it will give you the good feedback you need to improve quickly. Most likely, the rifle will be fine as is for your first season.
I would recommend that you get the trigger worked over (to a crisp 4.5#'s--the minimum allowed). Should cost around $30. It makes a big difference, especially in offhand. The guys at your local match should be able to point you in the right direction as far as who does good work locally--you don't want to pay a non-expert to work on your rifle. The local armorer will typically have a much quicker turn-around time than the larger outfits (such as Fulton). I've also got a pretty decent list of names and contact info of armorers if you need one.
Scott Duff's
M1 Owner's Guide is a good primer on the M1 and should go into the various match tweeks. Most of the modifications done to bring a rifle into match condition (a.k.a. national match--glass bedding, NM sights, unitized handguard, gas cylinder modifications) will disqualify the rifle for use in the CMP JC Garand Match (but that particular match isn't all that frequent anyways--maybe 3x a year around my parts if I want to drive 2 hrs--most matches are Highpower Rifle matches shot under NRA rules).
The best advice I can give is to shoot your first matches ASAP. Don't make the mistake of holding off because you don't have a match rifle, scope, mat, or other gear. The sooner you begin shooting, the sooner you'll start improving. Once you've gotten a little experience under your belt, you'll have a much better idea about how to spend your money.
Ty