I have recently completed watching a few high school dramas ( School 2015, With You, A love so beautiful). I was thinking of watching the Reply series because it looks interesting. But I don't know which one to start with. Are they inter-connected in any way? Which is the best or most preferred one?

I'd suggest you do it in the order they came out : first 1997, 1994 and 1988. The leads of 1997 have cameos in 1994 and so forth, so it'll be better appreciated that way. They are all good so you don't need to worry about starting with one that is bad. 

Thanks. I was thinking of starting with that one but I was very confused with the chronological order.

Yes, they don't have the same leads and the stories are not connected so you won't feel like you watching backwards.