There are Masses throughout the day. The largest Mass of the day is typically at the Altar of the Chair (ie, under the Bernini dove window) late in the day, around 5 if I remember correctly. On weekdays, in my experience, this is the Mass most likely to have a choir, if that's important to you. No ticket is needed, just tell the guard you want to attend Mass. They will rope off the area a while before Mass starts, to prevent disruptions of the liturgy. There are also Masses routinely at the Altar of St. Joseph (left transept area). Same procedure to attend. These scheduled Masses have been in Italian.
Finally, when the Basilica first opens in the morning, you'll find a large number of Masses being said at various side altars. It's the time when visiting priests are invited to say Mass. I've never had anyone object to my quietly joining one of those Masses, as space allows. And if language is important to you, you're likely to find one or more being said in English first thing in the morning. First thing in the morning is also my favorite time to visit the Basilica... for the quiet.
The only Mass that requires a ticket is a papal Mass, and if that's going on, you can't get into the Basilica without a ticket. But that's not an everyday event.