Some more tips:
1. Check in on-line with the airline from 24 to 1 hour before the flight. With boarding pass in hand, you may be able to bypass a long slow checkin line. At many airports, airlines will have a separate and faster line for checked baggage drop if you have already checked in on-line. If you have carryon baggage only and have checked in on-line, you can proceed directly to the security checkpoint once you figure out your flight's gate from the monitors.
2. Arrive at the airport with plenty of lead time before the flight. Follow the airline's suggested lead time for the airport, but add 30 minutes since you are a first time flyer.
3. Do not wear large amounts of metal or shoes that are difficult to take off and put on. If you have metal from knee or hip replacements or have needles for prescription medication (e.g. diabetics' insulin), get documentation from your physician. At the security checkpoint, place metal (keys, coins, cell phones, etc.) in your carryon or in a tray (with liquids and laptops separate), push the stuff into the X-ray machine, and then go through the metal detection gate. Keep a close watch on where your stuff is, since theft there is common, and the security checkers are looking for bombs and weapons, not thieves.
4. Wear clothing and shoes that you can easily walk or run in, in case you need to run for your short connection.
5. Keep with you or in your carryon a day or few worth of clothes (layerable for various weather conditions) and any essentials for the first few days, or if you have to spend the night in the airport after you miss your connection. Essential documents, ID, credit cards, etc. should stay in your pockets, since there are occasional thefts from carryons in airplanes.