Re: what size battery?
I have a 14' jon boat with a 40# trolling motor and 2 group 31 batteries. After 6 hours of constant trolling on speed 2 and 3, with the occasional burst to speed 4 and 5 they are ready to be charged. These batteries are 2 years old so I guess they probable performed better when new.
The lights really don't use much power compared to the trolling motor and since you are only going to use them for 15 minutes I wouldn't factor them in.
I really doubt you are going to get 8 hours of trolling on 1 battery, even pushing it on 2 batteries. It's really tough to guess how much power you are going to use, just yourself in the boat or 2 other BIG buddies, wind, current, etc... I'd get the biggest deep cycle battery you can (group 31) and see how one does (carrying a backup battery if you have one) then gauge it from there. If you buy a group 24 battery and it only runs the trolling motor for 3 hours you are not even 1/2 way to your goal.
My buddy has a 12' lund with a small Minnkota trolling motor and 3 group 24 (or 27???) batteries, I think he gets about 8 hours of constant trolling with his setup.
Remember when you add batteries to a tinny you should place them forward for good weight distribution, keep them at the stern and the boat will be stern heavy. Just balances the boat out better, makes it ride better and improves hole shot/getting on plane.