There is a lot to find out by ‘googling’ and checking out YouTube.
My English saddles need repairs, and I recently bought an ‘old-fashioned’ Morgan mare (14.3 hands and WIDE). I HAD a synthetic western saddle, but it didn’t fit her, and she Let Me Know It Didn’t. I read (online) and watched numerous videos to figure out how to measure her and get her what she needed.
That said, I ended up buying a 1979 TexTan Hereford saddle (has serial numbers showing model on the stirrup–made in December of that year), full Quarter Horse bars size. It is heavy but one of those older, well-made leather saddles. My mare loves the fit. That being said, even with a (possibly tall/taller) TB, you might need something narrower.
There are lots of western saddle styles available—cutting, roping, etc. I think you need to find something that you feel comfortable in. Mine is more of a trail saddle/all around type but there is no requirement to buy one. Just buy one that feels good to you and fits your horse.
I found my saddle on craigslist (local) for $400. Its sellers used to own and show Paint horses, so the fit worked for my mare. I sacrificed 1/2" for my butt, but it works. (Again, YouTube videos help.) My mare is short-backed, so it was important to get the right length in the skirt (see videos, again).
You may prefer a newer, synthetic saddle, but the good ones/brands ARE expensive. I lucked out by buying a quality made, OLDER saddle in GREAT condition. Saddle pads are what you want–I have a mid-range one that my cousin gave me. I opted to buy a second billet girth/cinch (usually needed if you do Actual cow work) simply because my mare bucked me off once, and I want to be sure my saddle stays put (paranoid me, she is much MUCH better). The main girth/cinch is what you want—to my inexperienced eye, I see very little difference in them, but someone else may have a more informed opinion on them. I have a simple western bridle/western snaffle that I bought at Tractor Supply. I use no tie downs, no breast collars, etc. I would not hesitate to use my English bridle, either, if I was just ‘putzing’ around, but the western bit was on major markdown/clearance at the time I was looking, so…
There are a heck of a lot more people more knowledgeable than I that may be able to help you here. I had not ridden western in 45 years. I still prefer trail riding in an English saddle, but this older, quality western saddle has been a surprisingly good substitute.
The Different Types of Western Saddles and their Purpose - saddleupcolorado