I bought a USGI SA Service grade a few years ago, fun gun to shoot. Going from box to first shot was relatively simple. I did a decent cleaning inside and out and was good to go.
A friend just bought a Danish SA service grade from CMP and had me look it over. The Danes packed these things in some serious grease. I had to detail strip the rifle down to component parts and clean the parts in Shooter's Choice to get rid of the grease. I also needed to strip and refinish the stock, because it was well coated with grease and the grease had seeped deep into the worn finish below destroying it. I also needed to repair the front handguard which had an arsenal pinned repair, but the crack had opened up again and I had to fill it will Acraglas.
The whole thing came out well. I'd like to run some JB bore paste through the bore to clean it up a little better, but we'll see how it shoots.
For the record, the Italian replacement parts often found on the Danish are EXCELLENT quality parts, at least equal to USGI in quality. The Danish VAR barrels are also exceptional. They are at least the equal of USGI service grade barrels and may be near match quality in some cases.
The real trick with the Danes is that cleaning them up for use takes some TLC and the beech stocks on many of them (aside from being ugly) are not as dimensionally stable as a walnut or birch stock would be. Beech wears like iron though and the instabilities are well within service grade specs, just not up to match grade. Polyurethane stock finish helps.
Springfield Armory made the most M1's so SA rifles are far more common than all other makers. This translates to lower cost from CMP and faster delivery times. IHC's, HR's and Winchesters can take a LONG time to get (over a year). So I would opt for a Springfield variant, a service grade to ensure better barrel condition, and if detail cleaning scares you, the USGI rather than the Dane. The Danes are entirely acceptable and I wouldn't hesitate to order one.