My nephew has one in 308 and I have one in 243. Great rifle for the price. More than good enough for Indiana deer hunting. Trigger is ok, but again for the price I can handle it. Never had any experience with Tula Ammo though.
I use Tula when I don’t want to pick up brass and just want to have fun. Great for that or getting a rifle on paper when sighting it in. Then I switch to something more accurate.
I have used 7.62 X 39 caliber Tula in AK's and SK's with no issues, however it doesn't seem as accurate as the premium ammo, but fine for plinking, I seriously doubt there would be any issues in .308 as far as function or any damage to the firearm but think accuracy may be slightly affected.
I would think for starting out, to get a real feel for things, use brass. After you are very comfortable, then try some cheap steel if you really want to. Get to know your new rifle before you try to figure it out using steel.....just my opinion.
Personally I have never had good results with cheap steel. Will never us it again. I'll buy the cheapest brass I can find when just range shooting.