In my experience living in places that tend to have more Western recreational (as opposed to “Western Pleasure”) riders than English recreational riders, MOST (obviously not all) horses that have been started under Western tack and ridden by the Western version of the casual amateur you are shopping for will adapt very readily to English tack, particularly if their training never got beyond a bosal or a snaffle. Not as easy to convert, say, a 4D barrel horse or critter that qualified for Western Pleasure at Congress, but something that’s been given a decent gas pedal, brakes, and steering. I used to ride with a H/J trainer that would hang around kinda low-end Western oriented shows (schooling shows, 4H, FFA, etc), look at ads at feed stores and the back of local horse “rag” publications (craigslist wasn’t much of a thing then, I’m sure he stalks that now) and pick up horses that had a good mind and a low asking price. Generally they had a low asking price because they weren’t stock-horse typey enough, fast enough for barrels, slow enough for WP, hadn’t been trained into a good slide, etc. to let their current rider move up in their Western field of interest. Which was, of course, just fine by him. He had a super-great “eye” for diamonds in the rough, though. He also just knocked on the door of a house with a skinny old rangy thing with his mane eaten off by llamas (really) and offered to buy him. That gelding was a high-point Hunter winner in his division (which, granted was low since he was an Old Man) by the end of the year.
If you and your buyer are feeling a little more adventurous, another avenue to check out is getting a Mustang. Right now the Extreme Mustang Makeover “circuit” is all virtual, but you can go to the webpage and check out the horses that will be available for the next virtual event upcoming in California, and get in touch with the trainers of any of them that interest you/your buyer (note that not all the trainers and horses are located in California). Many of the trainers that compete in the EMM are also Trainer Incentive Program trainers, and there are TIP trainers all over the country that may or may not be competing in any given EMM that might have, or be willing to pick up, prospects. TIP does not include saddle training, but a lot of TIP trainers are happy to saddle-start to whatever level the adopter wants for an additional fee. There are also some options for getting saddle-started horses through the prison programs and Mantle ranch (and probably some other “storefronts” I don’t know about). Obviously one can also adopt a Mustang as-is straight from the BLM and send it to an experienced trainer if one doesn’t want to deal with that part ones’ self, but that’s more of a pig-in-a-poke. With EMM and TIP options you can get more information on the horse’s personality and way of going, potentially even arrange for proper PPE, before committing. Most EMM/TIP trainers are Western-oriented, but see above. Some are better than others about focusing on the “basics” and not fussing over “putting on a slide,” and there are a few that are either English-focused or include work in English tack regularly (Sam Van Fleet, Elisa Wallace, Rebecca Bowman come to mind). Obviously all horses are individuals, but a lot of people automatically write off Mustangs, particularly young and/or green Mustangs as being too aggressive/flighty/spooky, whatever. My guy is probably a bit on the exceptional side (but I am biased). When I adopted him out of the EMM in 2017 (with roughly 100 days total training from holding pen to competition) I figured he’d need at least another couple month’s worth of full professional training before I really felt comfortable getting on him. A week after getting him home to let him settle in, my trainer worked with him for a bit and hopped off and said “Go ahead, get on, he’s wonderful!” Have we had our moments? Of course! But certainly no worse than pretty much any domestic horse I’ve worked with (the other day a barn mate got dumped when her horse spun out from under her for no human-perceptible reason), and heaps better than most.