[A4] new owner of 2000 A4 2.8Q...help!

[F550V12 at aol.com]

After thoroughly and repeatedly reading my owner's manual, I'm still unclear on one subject.  After I start my car, when I put it in gear, my trip computer reads "Service!" then goes away (to display the temperature, radio station, etc.).  However, at the top in yellow, the trip computer reads "OK."  Does this mean I need service or not?  And if so, what kind of service do I need?
 
I'm quite opposed to taking my car to a dealer unless absolutely necessary, as their service is generally expensive and requires a long wait.  I also didn't purchase my car from my local dealer, so I'm sure I won't be provided a loaner car.  Anyone have good advice for me?  Thank you.