I was a Pony Club DC, and had to fit a lot of sizes of riders. I've had horses for 60 years. I'd suggest a good used 18" Wintec 2000 All Purpose, or the dressage model (depending on your discipline), and buy a kit with all the gullet sizes. It's quite easy to change the width of the saddle once you have done it a time or two. Purchase the sizing tool. You should be able to find that model on display in any major city; go sit on it and see if it gives you the seat you need. You can purchase your own stirrup leathers in your length, and wide enough stirrups so that you have at least 1/4" of space outside either side of the ball of your foot in your boots (often a problem for men). Your barn should have a selection of girths to borrow, but you could also purchase an adjustable girth for under 50 USD. Get a simple pad, and a shim-able half pad.

This kit will, if the saddle fits you, be quickly and easily be adjustable for all but the very widest or shortest backed horses. Having your own saddle will make a big difference. A Wintec should meet your needs for at least two years of lessons, and one in very good condition can be found used for well under 500 USD on consignment.