If I encrypt (dm crypt, LUKS) my whole system, how many RAM should I provide ?
I've understood that LUKS volume is mounted RAM, ... If my system is 10 Gb, should I have something like RAM 12 Go ?
You have misunderstood. The LUKS data is stored on disc and encrypted/decrypted a block at a time as necessary (of course there is some caching going on).
I don't know the minimum size, but I operated a 32Gb LUKS encrypted ReiserFS partition from a 1 GB memory PC. A whole disc shouldn't make any difference from using LUKS on a partition.