I think the biggest thing if you are new to a sport and really want to be successful competing in short order, is to get a horse that is already doing what you want to do, successfully, and has been for at least a year or so and stayed sound with it. If you have a longer time line or low expectations and have good trainers/coaches to work with, you can muck about with young prospects and horses that are currently doing other things, but you are more likely to be ultimately unsuccessful in the new field and/or hit a bunch of roadblocks as compared to starting with what is the equivalent of a “schoolmaster” in the area you like. As far as where and how to shop, I’ve noticed over the years that endurance seems to be largely its own world and they don’t advertise in the more general-purpose venues like Dreamhorse very much. You are more likely to find horses looking in the endurance magazines and websites. Look at the ads, and also the articles for tidbits like “Samantha got Raydar +++ five years ago, from FireFox Farms.” Then you can look up FireFox Farms to see if they have any current sales you are interested in. Doing web searches, if you search “Endurance horses for sale”, and bypass the general purpose venues and dial in on the individual farms, you will find places like this: http://www.dealarabians.com/
Endurance has been dominated by Arabians and Arabian crossbreds for many, many years in terms of those competing to win, although there are certainly exceptions. I think there are also a large number of competitors, like marathon runners, who couldn’t care less about “winning”, they are just looking for a venue to give them goals for getting out there and riding/conditioning their horse, enjoying themselves, and getting a sense of accomplishment that they finished within some kind of reasonable time frame, and they and their horse are happy and sound at the end of it. Maybe as they go along they set a goal to beat their own time. Maybe their highest aspiration is a 50 rather than a 100. There’s a lot more variety of breeds and types of horses at that level. At that level, any equine you enjoy spending that much time with who is sane on the trail and sound of body would be suitable, and you can look a lot more broadly at horses that are in other fields but roughly similar exposure and workload (horses that are now doing Eventing, horses that are active working ranch horses, maybe even kids’ summer camp horses with some close vetting).