I feel pretty qualified to comment on this. I owned a 1998 Cavalier from 1998 up til late 2013 that had the same engine and it still ran great when I sold it. It had 359,833 miles and still ran GREAT!!!
As for oil, I went back and forth with Exxon Superflo Synthetic 5w-30 and M1 5w-30 in it for the first 10 years or so then I changed over to PP 5w-30 for the remaining time until I sold it. As for filters, I used Pure One filters by Purolator for the majority of the time I had it and eventually moved over to Wix after joining BITOG.
As for suggestions, you can easily run a synthetic up to 6,000 to 7,500 miles. Just make sure your oil filter game is strong. Also, make sure you cover up the exhaust pipe with aluminum foil or a homemade metal shield or something that won't melt when you change the oil so that the oil from the filter doesn't run out on it and get caught up in the braided flexpipe, which would give you that burning oil odor for awhile.
Had mine not been just a basic car with no options other than A/C, I would have kept it. As I got older, having no power windows, no power locks, no cruise control, no nothing started to wear on me. Would love to come across one at some point fully equipped so that I actually have an incentive to do repairs on it.
As 92saturnsl2 mentioned. Engine is extremely smooth. I miss that (my '03 Focus is no ways as smooth as the '98 Cav).
Lastly, at the risk of sounding "crazy" I could tell when the car needed an oil change (if I got lazy). I would feel a little bit of vibration in the steering wheel. Lots of good memories with my ol '98.
Anyway, that's my .02 on the matter.