the limit for riding beasts is the strength of the musculature and how it is organised. Now a peasant farmer rides a donkey with his feet dragging on the ground, almost; because the donkey has a very strong musculature, owing to evolving in the desert. A horse is ridiculously fragile by comparison and the legs are thin and spindly. But it can go fast.
Let's take a historical creature; the Hell-pig, about 30 million years ago. It was an omnivorous critter with teeth not unlike ours only much, much bigger - but it had a gape like a hippo and could crunch on bones. to do that it had massively long vertebral spines which were used for neck muscle attachment. The shoulder area of this pig-creature which was about 6' high at the shoulder, would be tremendously strong and could carry a lot more than a man, though I would think it would be both an uncomfortable and nervous ride.
reptiles? I'd think you'd want a python big enough to swallow a man whole to be rideable. I've seen people ride the giant tortoises of the Galapagos, they are tremendously strong, and the big ones are about 5' long. Modern lizards can't be ridden because of their splayed gait; but if you had lizards with straight down legs, then you could. It's more in the bone structure and the musculature than the size. Now, bear in mind that most of the larger critters anywhere tend to be the predators, if you plan to have a 10' salmon capable of carrying a man, because of the laws of evolution, somewhere you are going to have a 20' pike capable of eating it. And that is a whole new kettle of fish [sorry, I can't resist puns]
Or you might have herbivores which have grown big to resist carnivores; there isn't much which can take down an elephant, especially a bull elephant in musth .... and you have to factor in whether the mount wants to eat its rider, or if it is prey, and if so what the predator is like.
Insects? well, insects are tremendously strong for their size because of the chitinous exoskeleton. Now, this involves either lower gravity or denser air to get one up to riding size. Or higher oxygen percentage, which also works. Unfortunately this is bad for humans who suffer oxygen toxicity. Now a combination of lower gravity, denser air and a bit more oxygen - say up to 25% oxygen in the air - you could do it. And your humans would have to evolve to cope with it. the oxygen levels during the times of the great insects [about 35%] would be instantly fatal to humans. Any more than that and fires cannot be extinguished so it would be fatal to everyone any time a lightning strike set off a forest fire however adapted your humans.
I hope this is some use.