English saddles are better. I'm in a western saddle now because of my myopathy, but when I get stronger I'm going to be in an English saddlle. So you /can/ technically post, you just need to relax. You shouldn't be working hard to do it, just let the rhythm of the horse go with you and let his movement propel you up.
I suggest getting an exercise ball. They have books on exercises for horses. As for me, horseback riding takes care of a lot of core strength. Practice balancing.and cardiovascular activities are good. Even if it's not running or jogging, you can bike or jumprope to get your heart rate up. Contrary to what many people believe, even if you do sit-ups, your abs will grow stronger, but the belly fat won't necessarily come off. Your fat distributes through your body, so don't think locally, necessarily. Doing cardiovascular activities are very good for this, and just doing a little bit of something will help your heart and your center.
Another thing I recommend is swimming. Swimming is very good to help with your rhythm and breathing, because some people forget to breathe well and correctly.
Another thing is, do yoga, Take several minutes to go through your body. Go into positions as you would, or do it on your horse, and you might catch sight of some things that you didn't realise were tense before. If you relax and just put your weight in your heels you will find things a lot more comfortable.