I was stupid enough to just throw my saddle on the horse and hop right on. Which caused my horse to throw me many a times.
That should not happen, IF the saddle fits properly and you're placing it in the right spot on his back. I have switched many horses from western to english and vice versa and there was never a problem with the saddle. A "regualr" or "medium" tree English saddle will not, I repeat NOT, fit most American stock type horses. If you ride in one and your horse is anywhere near "stocky" through the chest, shoulders, and barrel, then your horse will very likely show his displeasure in the new saddle. This is NOT the fault of the saddle, the fault lies in the rider or trainer who did not properly fit the saddle before riding...
Also, an English saddle should set well back on the horse. The front d-rings should be a good 2-3" behind
the back edge
of the horse's shoulder blades. Only the front of the flaps (on an AP or CC jumping saddle) should overlap the horse's shoulder.
The big transition issue usually occurs if a horse was only ridden in a curb or gag bit. A plain snaffle (no shanks) doesn't have much bite, so you often need to "re-sensitize" the horse to a more mild bit. Some work in the arena or round pen on walk/stop transitions and lots and lots and lots of turning and circling usually gets your point across and helps the horse better understand. You also need to learn to use your seat and legs to control your horse, not just the bit. Using seat and leg will help the transition go more smoothly.