First, when you unrack the bar to start pressing, take two small steps back from the rack. There is no need to back up a long way from the rack, and indeed, it’s a waste of energy to do so. “Two half steps” is a solid way to think of the situation - a half step with the right foot, then a half step with the left foot - and you’re good to go. Stay close to the rack, and watch the included video (“Fix Your Stance…”) for a quick demonstration.
Second, take a relatively wide stance when pressing, and in fact, your squat stance serves pretty well for a pressing stance. If you’d like to go a bit wider than your squat stance, that’s fine too, but don’t take a narrow stance - again, watch the video above for a demonstration of what to do as well as what not to do. Remember, the press already starts a long way from your balance point (i.e., the middle of your foot), and it finishes even further from the balance point (i.e., up over your head), and as a result, the press is very susceptible to deviations in the bar path. It behaves almost like an Olympic lift (i.e., the snatch or clean-and-jerk) in this respect, and indeed, the press actually used to be part of Olympic weightlifting.
Because it’s so sensitive to bar path deviations, taking a wider stance (as compared to a narrower one) gives you a more stable base from which to press. Full disclosure - the wider stance doesn’t do a lot to help with front-to-back balance, but it at least helps eliminate any side-to-side balance issues, and every little bit helps in the press.
