Pick a rim width that is appropriate for the tire you are going to use.
Aero rims tend to be heavy, which is pretty much a negative for other than high speed use.
Handling is more tire and operator perception.

The approach I would take with an unknown rim to replace-
Measure a spoke. Both sides if a rear or disc hub.
Use a spoke calculator and determine an ERD for that spoke length and number of crosses. Just plug in different ERD's until you get the length correct.
Find a rim with that ERD.
The reason I'd work this way is your spokes might not be the "best" length as installed in the current rim. You may as well make them a "best fit" for the new rim.

Don't mess with old nipples. Wire brush the spoke threads.
That still won't give the "feel" of new spokes & nipples, but failure to do so makes the job much tougher. Nearly impossible if you are inexperienced.