-- Last Updated: Jan-01-13 11:07 AM EST --
Until you know how to paddle and have something that you are sure is a final boat, neither of which are true right now, something like what Tsunamichuck recommended or the relatively lightweight paddles from EMS with lightweight plastic blades will do you well enough. You can get those for about the price point you name. A really good paddle is well above that unless you find a deal used - more like $400.
It's not the time to invest in that level paddle yet. Your boat is quite wide - if you do get beyond beginner approaches you could end up with a much narrower boat anyway. The paddle that will get around a 31.5 inch wide boat may not be the same length as the one that would work well with a transition boat, usually a good 8 inches narrower than this boat.
As to feathering or not - get to some place for a few sessions on how to paddle correctly without hurting your joints. Two sessions early on could have saved a lot of new paddlers damage that can take a year to fully undo. And this will answer your basic questions.
To add - the drip rings in my experience do little to nothing to keep you dry, especially in a SOT. It is easiest to just figure it is a wet sport. If you want to try and stay dry, you can do so with clothing. But I doubt you want to write that check quite yet.