Your mind is in the right frame, but your terminology is way out of whack.
You want a 2-2.5" lift kit that rides smooth, but yet will tackle rough trails? Let's start with this. The smoothest ride you will ever have in a YJ is when it is on stock springs, any lift at all and the ride is compromised. Sorry, you cant have both. Some kits are better for a ride than others, hence the old saying, you get what you pay for. OME is about the best on the market for the 2.5" lift kit. But, its about the most expensive as well.
If you are only putting a 2-2.5" lift on your YJ then the 31's are the tire for that lift. If you want to run 33" tires, you will need a minimum of a 4" kit on it. Or when you go out to "tackle the rough trails" the tires are going to chew the fenders off the sides of your Jeep.
I believe that when you say "best suspension to go along with the lift" you are talking about shocks. The lift is the suspension. The best of them are extremely pricey. if you go with something like a Foxx reservoir shock, best bang for your buck are Bilstein 5100's.
As far as having stem/eye shocks in the rear? I have never seen a YJ with them on it. The rear if stock should have eye/eye shocks in the rear. If they have been changed to stem/eye shocks, they aren't stock. I would look at the frame towers for the shocks and see if they were welded in.
If you want a Jeep that is capable of only running a 2.5" lift and tackling tough trails, and still riding nice on the street? Sell what you currently have and buy a TJ.
'87 YJ, 4.2L built and bored, 8.5" of lift, 8.8 rear, AX15/NP 231, Tom Woods drive shafts, Flat fenders, 12,000LB winch, Custom bumpers, Rattle can paint job. Never completed...