Flight
There are two main airports in Puglia, Brindisi and Bari. Brindisi is closest to the venue, under 30 min away from the venue by car. Bari Airport is approximately 1.5 hours from the venue by car. Bari is the larger airport, so there are typically more flight options. To find the flight options, I like to use the flight connections website (link below),to see where you can find direct flights from, depending on where you are travelling to before/after the wedding.
Train
If you would prefer to take the train, Lecce Stazione is located in the Lecce city centre. You can fly into Rome (or another airport in Italy), and take a train directly to Lecce. The main train carrier options for long distance trains are Trenitalia and Italo. The link below is a great resource for train travel within Italy.
Travel Note
It really depends what your plans are before/after and how you prefer to travel. Rome2Rio is a great website where you can enter where you are coming from/going to and it will show you all the transportation options, as well as their cost and duration