Definitely no to a mini,
Since you've expressed you have high goals of competing, I wouldn't buy a horse at all, for probably a long time, as if you're only learning, you'll start on a beginner horse to learn, then something with more training, and so on.
If you want to go high, you will likely outgrow your horse, probably multiple times, with jumping especially, you'll likely learn on horses who cannot go any higher than a certain point, and since you will need to build up your own training, it can be better to work with horses at the level (rather than getting somethings that may be trained to do more than you're capable of yet)
If your true goal is competing, spend all your money on trainers/training/shows (the higher the shows go, the more expensive they'll get also)
Maybe just think about what is most important, and then go with what makes most sense.
I'm personally not a competitor, what important to me is having a bond, trail riding, having fun, really knowing my horse, I also get attached to things so my goal is to eventually buy, (leasing now) which for what I want, I think it makes sense. If I wanted to compete, and improve, and see how far to the top I could get, I'd be leasing horses that suited my level, then if they had their limit but I could go higher, I'd move on and lease something higher.
So just think about your goals, either way you decide, leasing or even a lease to buy is a good option, just so its not all overwhelming at once!
Good luck :)