What kind of climber did you get? Not related, just curious.
In regards to angling upward, you will have to do some testing in your lawn or somewhere first. Set the platform level, and see how tight you can hook your strap. Now, angle it upward and you will find you can secure your strap just a little tighter. As you climb the tree, the tree thins as compared to the base. While the bottom platform might be angled upward at the base, it will be much closer to level higher up. I don't think you will find as much difference in tree thickness from 15'-25' as you will from the first 5' of the tree compared to 15' up. That first 5' or so the tree will be substantially thicker than it will be at 15' or 25'.
USE YOUR HARNESS ALL THE WAY UP! I generally hook on once I am standing on the climber preparing to climb. Move up my rope, move up the climber, move up the rope, move up the climber. I won't start climbing until it is hooked onto my safety harness. It is not worth the risk of injury or death.