Hi Yzf... and welcome to the forum!!! 

What to look for all depends on what you're looking for (if that makes sense). 

If you are looking for something to shoot in Vintage matches, then anything that's in "As Issued" condition will do, so long as it's complete.  This can include rifles that have been restored or altered (i.e. switching rear sights and handguards, new barrel, etc.). 

However, if you are looking for a museum quality wall hanger, then that's going to be harder to find... and cost quite a lot more!

Good, As Issued shooters are out there, and won't break the bank either (under $1,500).... and there are plenty of very helpful - and knowledgeable people here who can help you along the way (Mr. Hosmer being one of the best)!