blind pew - If you have a smartphone you can buy an e-ticket through the Greater Anglia app. The apps of some other operators also have this function. The ticket works immediately.
Alternatively buy a ticket in advance from the website of any rail operator and collect it from a station convenient to you. Don’t wait until you’re in Southend as you’ll still have to queue! Having a ticket about your person also means being ready for a train should one come as soon as you reach the station.
To be fair, Southend isn’t the only airport station with long queues - I had the same at MAN on my first visit and quickly learnt my lesson.
Cant comment on phone reception- I’ve never had a problem other than at security where you shouldn’t be using it anyway though free WiFi is available.