For logic games, the best prep advice I could give you is to use LSAT logic games questions for practice. I was able to breeze through this section since the law school logic games are a lot harder. I would also encourage everyone to practice
atcprep on difficult and not medium as suggested above, as you'll be better prepared for the actual speed and difficulty on the test.
You'll need at least a month to see any genuine improvement, imo. I took two months to study last year, and tested on the second to last possible day. The result was worth it (class date next month). Don't be in a rush, and give yourself as much time as you possibly can to work on speed, accurate responses, memory, and stamina (the test feels like it goes on forever).