1998 Honda Civic LX

Hello, I recently purchased a car after alot of looking, I did the bumper to bumper pre-purchase check at a local mechanic before the purchase. They said the car checks out fine, but would reccomend to flush the brakes, transmission and a few other things, I dont have the paper on hand I'm at work. I was wondering should I find another place and get it checked out before I start, or should I try to do it myself. This is my first car and I'm not familiar with cars, but I pick things up fast. One other thing is the door locks unlock but dont lock when I press the automatic button. I read the article on replacing the doors I'm pretty sure I'll be able to do it, but I'm going to take it apart first and see if its just misaligned or its broken before I buy 4 door locks. Also any suggestions on maintenance or advice on what to do or look for to help prolong the life and keep the car healthy.

Thank you for your time.