The right oil.....??
 

Got a 96 civic ex and has 173xxxx miles. On the cap where the oil goes it says recommended oil is like 5w-30/40. Should follow what it says or put 10w-40? Doesn't leak oil at all.

5w-30

The only reason to use heavier oil in a daily driver is if it burns through a lot of 5W-30, in which case the engine is already worn out thus it doesn't matter much what you use.