If you want a WWII era rifle, then you'll have to go with a rack or field grade since the service/correct/collector grades are all post-WWII. The service grades and up will almost guarantee you a good shooter since the TE and MW will be good.
So it's a tough call. I'd always recommend a service grade or better for your first Garand. But if you want the WWII era rifle, I'd order a field grade and put a note on the form asking for a WWII serial number (ie: something 3 million or under). Usually the CMP will comply with reasonable requests.
It is true that the service grades may have the thicker post-WWII stocks, and often in beech or birch as opposed to walnut. Here's a picture of a service grade HRA I bought earlier this year:
Notice the European birch wood stock.
I bought a field grade SA and got a 2.51 million rifle. It shot really well, even though the barrel was graded field (I didn't gauge it myself so I can't tell you what the true TE and MW was; I still have the barrel though). So you can risk getting a field or rack and still get a fine shooting rifle.
As far as barrel replacement, new modern barrels go for as low as $150, and could cost you anywhere from $50-$100 for a gunsmith to install/headspace/ream the barrel for you.