Thanks everyone for the posts. I am definitely going to change all the fluids including, engine oil, transmission fluid, coolant and brake fluid. What I meant by full inspection is that I am going to go over the car completely from bumper to bumper. When I bought the car, I did do an inspection, but it wasn't as thorough as what I intend to do. Today I bought 2 Liqui Moly 10w40 MoS2 5-liter bottles (I'm not sure how much oil I need for the change, my guess is about 6 - 6 1/2 liters) and the MANN oil filter. I also bought a bottle of Liqui Moly Pro-Line Engine Flush.

*Liqui Moly is also known as Lubro Moly in North America.