Trees in the care of humans NEED pruning for health and aesthetics. When out there in the forest no one would care if the tree died because of an infection caused by rubbing branches, too tight of a canopy that causes fungus, growing too close to other trees so they are limited in resources...
If we plant them we most certainly should help them be the best they can be. This is a great tree and size to prune.
Number one: Pull that bark away from the base. Make sure that only the roots are beneath the soil, keep soil and mulch away from the trunk of your tree.
Number two: Clean your BYPASS pruners with alcohol and sharpen with a file. Do that with a pruning saw as well for anything over an inch in diameter.
Number three: Remove all branches that grow to the inside of your tree versus outward. Leave no stumps of branches. Cut them cleanly off right at the main branch.
Number four: Remove all branches that are drastically smaller in diameter in relation to their main branch. An inch thick branch with 1/4 inch branchlets for instance.
Number five: Remove all branches or at least one of two branches that are touching each other.
Number six: Remove all branches that look wimpy and don't have healthy leaves.
Number seven: Chose a leader. The main stem that will form the natural form of your tree. When you get your tree thinned using the above six numbers, send a picture of the remaining large branches and I can guide you from there.
Get a smallish tarp; 10X10 feet? Throw your branches and debris on this tarp as you work to drag away to compost or dispose.
Stand back and LOOK at your tree as you work, take a sip of water or whatever. What is this tree btw? Send better pictures of leaves, buds...what color/kind of flowers have you seen on this tree. Ask your nursery what it was that you bought. All trees have a very identifiable form that should be honored unless you want to drive yourself crazy making an artificial form. Never HEAD a tree unless to remove weight from a too long branch. You will be thinning this tree. The rule is to never remove more than a third of the vegetation or photosynthetic growth per season. Less is better but from what I see you won't have to worry about that. When unsure about a cut. Don't. Send a picture instead.
Send a picture of the bottom of your trunk after pulling the mulch back.