I advise borrowing tack to start, but if you do want to buy, an all purpose type saddle is probably your best bet until you decide if you want to specialize further into jumping or dressage. I bought my no-name AP saddle on eBay for $120 + s&h, (Saddle, stirrup irons and leathers, and pad), and my plain raised snaffle bridle w/ laced reins at TSC for something like $30 (uber good sale, they were getting rid of all the English inventory). The shape of your pad doesn't really matter unless you're showing. Too many pads can cause the saddle to pinch, just like western. If you do buy a saddle, remember that English saddles are measured differently than westerns (usually a couple of inches larger: I personally ride a 14-15 inch western and a 16-17 inch English). Your nylon bridle will definitely work if you aren't showing.
One tip: Take a leather curb strap (no chain) and run it through the front dee rings of your English saddle as a grab strap if you feel unbalanced. It took me a little while to feel really secure without that big western pommel and horn in front of me.
Good luck and have fun!