New Riviera owner

My name is Charles and I live in Knoxville Tennessee.
I bought a 1998 Riviera last week. 187k miles but in really decent looking shape, I think.

I'm excited. I've wanted one since I first saw one up close in 2005. It's been a dream car ever since.

I looked for 2 or so months and found this Riviera local. As I looked I noticed ZERO Rivieras on the road in Knoxville.

I think I will start with an oil change but where to go from there.....?

Well, I'm here now and ready to learn.

Welcome,
Fluids are a good first move for sure, these cars are quite reliable even with high mileage.
The amount of maintenance/care it has had really dictates what the car needs. if you have any records of its past and or its obviously been maintained well it should be as any other car.
If it runs well and no lights on the dash you should be good.
Good luck!
Jbird

Welcome aboard.

I would look at the belt tensioners.  With your mileage the tensioner pulleys may need to be replaced, and perhaps the tensioners themselves, if it hasn't already been done.  And the belts, of course.  This is not a fun job, but I managed to do it.  

I also changed the fuel filter and air filter when I got mine.  

There's also a few things that could stand to be lubed - all the window, door, trunk seals, the tracks for the windows (have to take off the door panel, it's not that bad), the seat rails, the sunroof if you have one.

The Sweet Project Cars channel on YouTube is a great resource, just to give you an idea of what can be done to maintain or clean up your car, and how to do it cheaply.

Welcome Charles

Welcome