Get the longer one. Get the one with the most power that you can afford. The slightly longer shaft might interfere with your casting once in a blue moon - get over it, learn a roll cast, or a pitch cast, or a side arm cast, maybe back handed. The longer shaft will let you drop the motor a little deeper when you're in a little chop.
I assume that with the 15" Jon boat you're going to go with a 12 volt motor. The BPS 2019 Master Catalog, (one of my bibles and among the most favored of
rest room reading material ), lists the Minn Kota Endura Max 55 ? thrust, 36" or 42" shaft, for $289.99 and the 42" shaft is $10 more. If they're out of the long shaft, get the shorter shaft, but I'd get the longer one.
Be aware you're not done yet. While you're at it, pick up a few extra shear pins, most hardware stores carry generic shear pins, get one that fits if the store you buy your motor at doesn't carry extra shear pins. Keep the pins (and the necessary tools to change it out) in a bag that ALWAYS makes it into the boat.
Got to have batteries - get the largest deep cycle trolling motor batteries you can find - when I was fishing out of a similar boat years ago, I had 2, then 3, wired parallel, so I still had 12 volts, but lots of spare power. Running out of battery power isn't any fun. Each boat is different, so you will have to find the best balance point in your boat on where to locate the batteries. It isn't always snug up against the transom. When you need extra wire, I've found the easiest solution is to sacrifice a cheap set of jumper cables of the appropriate length. Clips are bad, curt those off and rig all your connections with rings that tighten to the batteries with wing nuts. Much simpler - solid connection and are much less likely to come undone at inopportune moments.
Those batteries will have to be charged. When I had a similar set up to what you've got, I bought a 2 bank charger, when I went to 3 batteries, I got a 3 bank one. These are marketed as on board chargers, but you don't have to install them, you don't need the extra weight on that boat - leave the charger at home. The multiple banks just make it much easier to charge all the batteries at once (and leave them charged) so that they are ready when you're ready to go fishing.
2 batteries & one charger just guarantees that you'll forget to switch it over and you'll end up charging one battery longer than the other and running 2 batteries with different levels of charge just lowers the life expectancy of both batteries.
Learn how to take the prop off and change out the broken ( or most likely badly bent) shear pin and carry the tools in the boat to do the job. Most likely if the shear pin is badly bent, the prop ain't coming off with the tools you got in your boat, but that's a different problem.
Good luck with your fishing. When you go from oars/paddles to trolling motor power you will get a lot more fishing done. Don't leave the oars/paddles on the bank because sooner or later you will need back up power.
There you go - that's it - all I know, from personal experience, about attaching a trolling motor to a Jon boat.
Nope, there is more - you will need to find a way to keep the batteries solid & stationary while you're running the boat, more importantly while you're trailering the boat. You don't want the batteries bouncing or sliding around while you're going down the road. What I did was to epoxy metal loops to the inside hull of the boat and used bungee cords to keep the batteries together and stable. Battery acid is an issue over time - just buy new bungees every season or so.
Glad I could help you spend your money.