I would wait until fall to plant it, Meghan. July and August will be hard enough on that little tree, without adding transplant shock to the mix. You don't have to wait until all the leaves drop, but at least wait until the nights are cool and days are shorter.
You should always prune off suckers if they are coming from below the graft - that will be a bulge in the trunk fairly low down. They will just take energy from the tree. Also . .
You're going to hate this but . .
You really should take off the immature fruit as well. The tree will then put energy into growing healthy roots and new leaves rather than into making fruit. You will get a good crop sooner in future years if you do this.
