How does one use the stug like the germans did IRL? Put it in infantry divisions for a kind of space marine esque division?
Well, the TD doesn't represent assault guns perfectly, but in terms of in-game representation... kinda.
The assault gun battalions were in theory intended to be allocated to infantry divisions on a one-to-one basis as organic support, as you describe. In reality, there were never nearly enough StuG units, and they were usually reserved as a Corps-level asset, and then they started using them as stop-gaps to fill up the Panzer Divisions to strength, and then.... Yeah, they never really got close to the theoretical organisation IRL, but the theoretical organisation would've been along the lines of including a MTD battalion in you main infantry template.
Edit: as noted above, this will indeed cause you very high StuG losses if you do it in game because the game doesn't deal well with very low equipment numbers in a division (and the TD battallion doesn't use many TDs). Using a smaller proportion of your inf divisions with a two-battalion commitment instead of one each but for more should in theory be much stronger for a few reasons, and is historically justifiable.