here is my opinion on the matter, as I have done some research and have decided to get back in shape. I actually believe that being out of shape the last 6 months or so has negatively impacted my pool game in some big ways.
#1 You need to focus on core strength and balance, this is going to help your pool game tremendously.
#2 Focus on doing exercises that take skill and balance to do properly, this will help your focus and strength.
#3 Forget about working out your arms specifically, it will hurt your game and it's typically unnecessary unless you just want huge biceps to impress the ladyfolk... important, but they prefer a well rounded physique.
#4 Do endurance training rather than strength training, this is going to help your endurance in long sets on the table and help you bring your focus up. If you can keep a mental edge for longer you have a huge advantage over the competition.
#5 STRETCH ALOT! Not only will this help with the soreness, but it is going to keep your muscles loose and flexible. This is essential to good pool. If you watched the Mosconi cup and saw Shane shaking out his hand... that's because he was trying to shake the tension out of his body. A totally relaxed body and mind are essential to playing great pool. Add some meditation into your stretching and try to clear your mind. Obviously, Yoga is a great way to do this but it's not for everyone.
Really you want to go "Bruce Lee" style of fitness... not Schwarzenegger. If you can achieve clarity in your mind and relaxed coordination between your muscles and brain then you are way ahead of the game.
These are only my thoughts, but I feel strongly that your game will only improve if you try this. At first your game will fall off while adjusting, but you'll make it up and then some very quickly.