We had a 1998 Civic and gave it to my nephew when we bought a new 2007 Civic. The car now has 220K miles and is still running great. Depends on how much you want to spend & how often you like doing oil changes, but both oils (conventional or synthetic) will do great in that engine.
I would stick with a 30 weight oil cause when I tried 5w20 oil to see if it would help bump gas mileage a bit.....the engine not only consumed oil but gas mileage dropped.
Switched back to 10w30 and consumption went away and gas mileage increased.
If you get a 'Check Engine' light, check to see if you have a cracked exhaust manifold as this is a well known Civic problem at your mileage. No need for fancy spark plugs, just use the copper V-Power NGK plugs.
BTW, the largest oil filter you can use on that car is the Purolator L-20073 or Wix 51347.
You never mentioned what type of Civic you got: DX/LX, EX or HX ....and is it 5 speed or Auto ??
I have lots of good maintenance tips if you need more, but with basic maintenance, that Civic will be on the road for another 200K miles.