In colloquial English usage, "get the best of" means to beat whilst in competition, to win to achieve dominance or superiority in some regard - "we played table tennis, and I got the best of him two out of three matches", and is sometimes shortened to "bested": "we raced, running hard, and he bested me".
However "to get the best out of" is used to mean you found a method to get the most effort/work/efficacy out of a given person, item or event: "Her teacher was brilliant: with careful planning, despite her detesting the topic, he got the best out of her and she took first marks as a result" or "we raced, my son and I, and by running neck and neck, dropping back and surging forward, I got the best out of him; he ran as though world's ruin was at his heels".
So in your case, the only appropriate phrase of the two presented is "get the best out of", but be aware that it connotes that there are special techniques, tricks, or not readily apparent ways to accomplish the tasks at hand.
Hope this helps.