Make it a point to reach the theatre at least 30-40 minutes before the scheduled time. Most theatres don't allow late seating anymore, which means you'll have to watch the show on a monitor in the lobby until intermission or the first break.
The simple answer is anything. Most theatres no longer have dress codes, so it doesn't matter what you wear. As long as you have a ticket for your performance, you'll be allowed into the venue.
You can bring a backpack into the movie theater, but you will be asked by the usher at podium to open your back so that it can be checked with a flashlight to ensure that nothing is being snuck into the theatre, like a gun for example.