I'm not sure what you mean by +12 AP? Do you mean the epic red +20 one or the blue red +16? If it's the +16 you should do 8 str anyways.
I would suggest gemming for max dps for 2v2 and 3v3. For 5v5 the same thing, unless you're on a serious and high ranked team (in which case you wouldn't really be asking).
So, max dps is basically go all out of AP if you have low AP (probably) or heavily into crit if you have great gear. I'd say make the leap around 1600-1700 AP for switching over, but there's some much better dps opinions than me on that. With a all-season 1 gear set (honor now), I'd go with just 24 strength in there or a 4 str 4 crit in the yellow to pick up the extra crit.. I agree with the 150 hp enchant if you want to just hold off on spending money till later. When you get s3 chest (assuming you're still in mostly s1 gear and lower than my AP number) I'd stick with the same gem setup as you used before but switch over to the stats enchant since you won't be getting rid of that soon.