"Brush up on" is a fairly formal and colorful expression but I see no reason why it couldn't be used in formal communication. It's universally known, and perfectly pleasant. I would use it. If you still have any doubts, though, then say "it will help me to become more proficient in ..." You want to say "I made a conscious decision". Conscious, in this context, means that the decision took place in your conscious mind and not in your subconscious, or instinct, or gut. Conscientious is to do with your conscience: your sense of right and wrong. Jiminy Cricket represents Pinocchio's conscience, and helps him tell right from wrong. A conscientious decision would be something like deciding that you don't want to take part in a war because you don't want to hurt anyone.

it will help me to improve <whatever it is, e.g., "my English", "my guitar playing" etc.>

I'd tend to agree with Steve, but you could also use "review."