I'd say go make mistakes and learn from them — it'll happen very quickly. If you say дом (house) as дам (which means "I will give"), the person you're talking to will correct you almost immediately. If you try to always pronounce "о" as "o", that will work as well; people will always understand you (even though you'll sound like a 19th century dweller of the Volga-basin area).

But I'll add that pronunciation should be the last thing to worry about for anybody who's learning Russian. Grammar — that's what a learner should be focusing on. It's so much more convoluted in Russian; English would feel extremely liberating in that regard.