[NoDOHC]

Congrats and welcome to the club.

You might want to check/change your fluids, inspect and replace all cracked vacuum lines and generally get to know the lay of the land on your car. Like all 1989 cars that you will buy these days, it will have a few idiosyncrasies.

I would research and pick the method you like best for cleaning the carbon out of the engine and the intake ports (I prefer removing the intake manifold to clean the 5th and 6th ports out, then I can free up the actuators and get everything working properly).
I get the engine warm, rev it and let it pull water in through a small vacuum line (the cruise control one, usually). This cleans the carbon off the rotors, some use ATF, some use Marvel Mystery Oil, take your pick.

My experience has taught me that the S5 NA rotaries usually die of carbon lock, sometimes from gradual buildup seizing the apex seals and sometimes from injesting a large amount of carbon from the 5th and 6th ports opening for the first time in a long time. Either way, you need to get it out.

You should also find the FSM and get to know it. (Learning how to operate the search tool is also very helpful).

Welcome again, I am sure you will enjoy the 'vert!