Your first quilt..... congrats!! You're getting some good suggestions but I'll add a comment or two.
1. Do square it up and add a border to help with keeping things nice and straight... and the binding issue.
2. When you have it sandwiched and ready to quilt, be sure to use a walking foot so the top doesn't scoot and you get tucks. You want to keep things as smooth as possible. Start in the middle and stitch to the edges. If there is any shifting, starting in the middle helps. I find that keeping my stitching lines parallel and moving out helps too.
And we'll be here to help you with the binding when you're ready.