To get out out the cockpit, I reach slightly behind my back, put my hands far to the outside of the rear deck (where there is some nonslip tape), and push up and back so I can slide my legs out.
Which muscle groups in the arms and shoulder are being used to do this?
I am trying to pick out the right piece of equipment at Planet Fitness…
The primary exercise for the group of muscles you are using would be dips. If the gym doesn’t have a machine you can use the edge of a bench. Or two benches side by side to mimic your hand placement on the cockpit edges.
You can modify the exercise to the depth of the cockpit if a full dip is too much for you.
Talk to a personal trainer and make sure you are using proper form to stay safe and get the results you want.
Pecs, triceps and deltoids, as @Tracerbullet said the best single exercise would be a dip. Additionally, almost all movements are safer and easier with an activated core, so exercises aimed at your core would be valuable too.
Yes. What he said when it comes to paddling the boat. Also, if you have long portages/carries when you are out of the boat, it helps to do some squats, lunches, or a stair climbing machine at your gym.
Overall, for any physical activity and general strength, it just helps to have a regular balanced routine that alternates workouts for your upper body, core and legs/glutes. Most folks can’t paddle to “get into shape.” Rather, one stays in shape to have better physical ability (but not same as “skills”) to paddle.