I would suggest even to those who don't wanna be oly lifters to train at an oly lifting club instead of some random gym. In general the atmosphere there is going to beat out the tons of machines at the gym which you don't need anyway.
Your program looks fine as long as you squat twice per week at least.
Stretch/foam roll = the more the better. If it hurts when you foam roll it, then you probably should foam roll it. If it's tight it also probably needs stretching and/or foam rolling.
Try to find stretches for everything butt and below. As long as you feel a stretch in the muscle that you are trying to stretch that's good enough IMO. 4 sets of 30 seconds for each muscle is more than a decent amount of stretching if you do it every day.
Supplements, I suggest the same as the others, but.. find a GOOD fish oil, otherwise you can be spending a lot of money which isn't worth it. The one from Biotest is pretty good and if you are in the US its probably at a decent price. I'd start with 5grams of EPA+DHA combined per day.
A good multivitamin is also great. If you tend to feel sick often then definitely get vitamin C supplements. Other than that I suggest protein, creatine, glutamine and BCAAs in that order. Start with just protein and only during/post workout. Most important part for you right now though is to just lift often with proper technique and get your diet/sleep right.