Lot of good advice for you. The only thing I might disagree with is that you can make a good horse or mule out of any breed. I think you can make them useable, but certain breeds aer more ameniable to certain task than others. That is the basic reason different breeds came about.
Thorbreds are bred ot run/jump.
1/4 horses are bred for agility,cow sense, work ethics etc.
Fox Trotters, Tennesse Walkers,Paso Finos etc. are bred for smoothness of gait.
Percherons are bred for heavy work.
Arabians are bred for endurance.
And so on and os on.
Just about all breeds can do any of these jobs, but each of these are more suited to thier intended task, but every once in awhile you can find a horse or mule that does all very well and that can usally be attributed to thier disposition, the trainer and the way they are handled.
There is a HUGE difference in what is referred to as a Missouri mule and Missouri Fox Trotter mule. The Missouri mule is usually referenced as one that has been bred from some type of heavy horse, ( usually belgiums) and a Mammoth jack.
The Missouri Fox Trotter is a gaited small framed horse and produces like mules.
In the mule world for the last several years,the buzz word has been gaited mules. Peopele tack big money on a mule if they claim it is gaited. In actuality, most mules are smoother gaited than a horse and when used in mountain riding, a gaited mule doesn't add much because you are negotiating rough, steep trails. The gaited aspect only comes into play on those not so treacherous trails. Nothing wrong with a nice smooth gaited animals when you want to cover a lot of ground fast.
I have people come up to me and the first thing they ask is if the mule is gaited. Then further talks,I find they don't know zip about a mule.I don't waste anymore time on them after that.
If one set his mind to it and commits you can do most anything with any breed. However, as you referenced some are quite better than others.
We had a champion bucking horse that was in our dude string. He was as safe as any seasoned baby sitter.
I'm beginning to make a "string" out of these Rocky's we manage and things are going well. However, I prefer Mustangs and mules for "string".
Gaited horses are fun when you have the terrain to use them. I've enjoyed every minute teaching these gaited ponies to navigate the hills. One thing I do see as an advantage is even when not using the gait they have a longer stride and still average a faster speed over all. Truth be told in teaching this pony "Dawn" the ropes... I hardly if ever used her gait.
I whole heartedly agree that a mule is one smooth ride. I do very much enjoy a good saddle mule. The wife and I intend to purchase a few mares from the owner of the ranch we manage for and will breed them to a Jack to find out for ourselves what can be discovered from gaited mules. That's a 5 year thing though.
To the OP.
I think if you invest the time and do it right you'll have no regrets and discover an entirely new freedom to run the hills. Even in consecutive days without ever coming home. Some get it, some don't. Those who do are addicted. Those who are addicted know what I mean.
