You should probably invest in a few lessons first just as a refresher to get your seat and balance and cues back. That would be the safest way to get back. Then discuss with your instructor the type of riding and classes you are interested in and ask for some recommendations for saddles and tack. For hunter jumper and flat you'll probably want a jumping saddle (sometimes called a close-contact - though close-contact actually only describes the panel-style), or an A/P that's has a nice forward flap and a not-too-deep seat.
As for saddle advice, I'll refer you to this recent thread. I'd put the Kincade in about the same class as the Regent asked about in this thread. Regent Saddle
Make sure your saddle fits the horse right. So make sure that whatever you get can be tried and returned if it's not right. This is much more critical on an English saddle than a Western. English saddles are not forgiving in their fit.
There's a sticky at the top of the Tack and Equipment forum here called: "Does your saddle really fit", and it has the 9 Schleese fitting videos, which is a good place for you to understand before buying a saddle.
In addition to the saddle, you'll want reins that are 1-piece - no split reins. You'll need a snaffle bit, and a headstall with a cavesson noseband.