This is a great thread. As a first time owner (for about 6 months now) I am finding many of these tips very helpful and wish I had read this before!
My advice would be.. Remember that YOU are your horse's advocate. If something feels off or just doesn't look quite right, don't just go with someone else saying they're fine and you're crazy. You probably know your horse best out of anyone.
I was kind of surprised to find how much time you really need to wait to ride in the beginning. I was DYING to ride my new horse, but everyone really said to stick to groundwork and build a relationship. Now, we are dealing with a lot of respect issues and I wish I had spent even MORE time on the ground. It's a lot harder working backwards than doing it right the first time.
If you ever feel in over your head, don't be too proud or embarrassed to ask for help. Sure, you don't want to feel "stupid" or like you can't handle something... But you and your horse can work through something a lot quicker and safer with someone else's help. (The RIGHT "someone"... Don't trust everyone you meet)
Always keep your ears and eyes open. Try to absorb everything around you. You can learn so much just spending a day with your other boarders, watching them work through something, going to a local show, etc.
And lastly... Be confident, believe in yourself. I know for me, there are times when I feel like a complete failure. Just take a step back, breathe, and remind yourself that you can do it. Maybe not alone, but it's not the end of the world.
"No hour of life is wasted that is spent in the saddle." -Winston Churchill
"Strong legs, soft hands, steady mind." (Unknown)