1995 Honda Civic Motor Oil Choice!?

I have a 1995 Honda Civic lx (four door) with a D15B7 engine (standard). It started burning oil about a year ago (do to a failed piston ring in cylinder 2). I don't have the time or money to replace it, so tough luck. The current oil I have in it is 10w-30. I am past my last oil change, I am trying to decide on what kind of oil to get because of my circumstances. I was thinking somewhere along the lines of 20w-50 (synthetic). winter is coming up and I live in Wisconsin. So I was considering getting a less thicker oil, but I have no clue.

I've read up on oil and I just want to play it safe by asking some professionals!

Burns Oil in idle, but you can faintly smell it, can't see it. Under slow acceleration, it progressively gets worse (maybe a small amount of black smoke). Under Heavy excel (such as getting onto a freeway) Black Smoke out the back and heavy oil smell (looks like a diesel slowly accelerating, not thick black smoke).

if your goining to synthetic i use pensoil you can also try regular oil 10-40 and put some castroil honey oil in it for what it's worth. are you sure it's the rings gone or valve seals?

Why waste synthetic? Buy the cheapest 10w-40 u can find and throw in some engine honey.