I use the cheapest synthetic blend oil I can find ($60/ 6 gal @ Advanced Auto). I also send oil samples of all my vehicles into Backstone (Blackstone Laboratories | Oil Analysis - Learn What's Going On In Your Engine) and have not had any bad contaminants in my oil. I also have a mechanical oil pressure gauge that always stays steady. Unless you're drag racing with some serious HP I wouldn't spend the extra money.
so always go synthetic? because my dad, before i had the car, would put conventional 15w because of an apparent oil leak. idk why he didn’t just put the synthetic? and would it be bad if i put synthetic with the 15w
One of the benefits of a synthetic oil is increased longevity between oil changes. I HIGHLY recommend keeping to the recommended oil viscosity (oil weight) from Honda/Acura. Moving to a thicker oil like 15w due to an oil leak is a band aid to the problem. Any engine has strict & tight bearing tolerances that require a specific oil weight. Going thicker might yield results where you have metal to metal contact due to the oil not being able to enter those tight tolerances.
My recommendation: Fix the oil leak, and use the recommended oil viscosity for your motor.
I use 10w30. I had a leak/seep from the valve cover (which is common), so I would change the valve cover gasket every year to two years, when I would notice it again.
That aside, syn and syn blend oil is THINNER than conventional oil. That said, using a syn or syn blend will make your leak worse, not help it. On one hand, that will help you find it, but on the other, worse leak. So yeah, that's up to you. The stock motors in the integras were made for conventional oil. Syn and syn blend is only better in that it doesn't break down as fast as conventional oil.
If you are driving normally, and changing your oil when it is supposed to be changed, there isn't any reason to cough up the extra money for syn or syn blend, if you haven't considered it until now. Another thing is that going from an engine that has run on conventional all of it's life until now, to using syn or syn blend can potentially be bad for the components.
There are a lot of published studies and articles about the syn syn blend vs conventional oil discussions. I would stick with what you are currently on, but use a 10w30, until you are better informed to actually do a switch. Especially if your engine is stock, and has over 50k on it. 15w oil has its applications, but in a Honda motor generally isn't one of them. It isn't a 1974 Ford truck. -_-