The MSI GPU is that quiet without further modding, or do i need to control the fans in some way (besides the way the card doses it itself)
The MSI continues its well rewarded tradition: after the R5770 Hawk and GTS 450 Cyclone, the R6870 TF II OC can be run at stock very quietly. MSI Afterburner is an added bonus, if you mind.
would that kind of card fit the SG07? (being twin slot)
IIRC it's the most compact high performance solution available (though Gelid & AC are triple slots ones): however, it fits.
But if I were you, I would be more minded (more than on GPU) about how to address the top fan and the PSU noise, particularly the first (as you won't have a rheobus or enough controllable fan headers on a mITX mobo: even if with a low power CPU - 2390T, 2500T - you might get rid of). And I would be very cautious on the CPU heatsink clearances, as there aren't so many high performance ones under 115mm while being not so wide (some 1155 mITX may have a relatively odd socket placement, check twice): the very first candidate should be the Thermalright AXP-140, maybe with the optional TR Universal Vault (aka Venomous BTK), but YMMV (look at the HDD bay, a 140mm fan might easily interfere with a 3.5 drive). If you drop the top fan, MAYBE an NH-C-14 could also fit.
Obviously you may go for a low performance one, like the Scythe Samurai ZZ or the Big Shuriken (maybe swapping the fan with a regular SlipStream) with relevant mountings, saving some bucks and space, but personally I wouldn't recommend them with a >65W (TDP) CPU.
Eventually, if you aim at a true quietness, such a setup won't be such an easy day, and however you are likely to build a relatively very expensive system (particularly if you shouldn't like the PSU tonal quality). If you dont' mind about that, a Lian-Li TU 200
would look also very classy for a student (but you have to choose carefully a storage strategy).