I think you can be a beginner and still have a horse, but I also think you should be more of an advanced beginner and be bloody **** sure you have the orse that's right for you first. As a rule-of-thumb, QH's are really good, but don't go by just that. Any breed could be fit. Make sure oyu have yourself a good, sturdy, been-there-done-that horse who can teach you and make sure you have a human teacher too.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.