How exciting for you! Your arrival plan to get from curb to gate will depend on a number of issues and should start long before you get to the airport. Assuming no special needs and packing only toiletries, shoes & clothing, here are my suggestions.
1. Check-in online 24 hours before your flight to get the best possible boarding number. you can print at home or at the airport.
2. Make sure to have your government ID with you.
3. Plan for an early arrival. 1.5 to 2 hours before departure is probably enough time. Boarding is typically 30 minutes before departure, getting through security about 30-45 minutes and checking bags about 30 minutes.
4. Consider whether you want to check baggage or carry it on. 2 bags are free on Southwest and you check them at the Southwest ticket counter inside the terminal. Check out the baggage rules here: https://www.southwest.com/html/customer-service/baggage/index.html?clk=GFOOTER-CUSTOMER-BAGS Size matters in carry-ons, plus see notes about liquids in the next section.
5. Getting through security. Look on your boarding pass to see if you have been randomly selected as TSA Pre-check or not because that drives what line you get in. (a) show your boarding pass and ID together, (b) one quart size ziploc bag with no liquids bigger than 3.4 ounces, (c) laptop in its own (TSA provided) container in line,and (d) if not TSA pre-check (with first flight, you probably would not be pre-check), shoes, belt and jacket off, everything out of your pockets, (e) go through screening and put everything together on the other side. Information available here: https://www.tsa.gov/travel/security-screening
6. Get to the gate area, get water if you want, use restroom in the terminal (much better than the plane), note your boarding position (no assigned seats for Southwest) and wait for them to announce the boarding.
The Memphis airport has a website that addresses common issues - check out these pages:
http://www.flymemphis.com/dropoff-pickup
http://www.flymemphis.com/airport-security
Southwest typically flys out of terminal A in Memphis.
Southwest has a long list of frequently asked questions that might be useful.
https://www.southwest.com/html/customer-service/faqs.html?clk=GFOOTER-CUSTOMER-FAQ
My suggestions are very high level and assume no delays due to weather or large travel events like a big convention letting out all at once or Memphis having some big festival on Halloween. I can't cover all the issues but I hope I hit the highlights for you. Best of luck and safe travels.
