If you aren't too familiar with some of the minor leaguers, I recommend a crash course before you go. Buying a program with photos or jersey numbers could be helpful, too. They occupy the majority of the fields at any time and are more than willing to stop and sign a ball or say hi on their way off for the day. There's work going on on 4-6 fields at any given time, so it's hard to keep track of who you're seeing. I took my 5 and 6 year old two years ago and besides "Papi" and "Pedey" their knowledge of Red Sox players was somewhat...um...limited. But they had an awesome time getting balls signed by all the 18 and 19 year olds who were often genuinely surprised they were being asked for an autograph - including Devers. The access is so great. There are bleachers around each home plate area, but the fields are so close you can really just kind of meander back and forth based on what/who you're trying to see. At one point, I had to call my kids away from chasing down the inordinate number of balls some scrawny little lefty was pumping over the RF fence of Field 4 because Price and Porcello were signing as the came off Field 2. It was once they'd moved on that I went back to see who had been hitting and discovered just how small Benintendi was.
The big leaguers are a little less accessible. When I was there, the majority of their work was done on Field 1 and the agility field closest to JetBlue, which is roped off at the end. But as they move from place to place, it's almost like they designate two or three guys to stick behind for a few minutes each time. We did the tour of JetBlue, and besides getting up onto the Monster it wasn't terribly exciting (shocking with all the history there, right?). The one thing it did, though, was allow us access to a simulated game that was going on. Got to watch Vazquez throwing home to 2nd at 100% for the first time since TJ. Then watched Price drill him in the back. Apparently, they often offer those tours during pre-game BP, too, which isn't typically open.
Parking isn't terrible. You pretty much just park and wander in and around as you like. I would recommend trying to find game seats under shade. We watched one game from great seats along the 3rd base line (my wife snagged the lineup card from Lovullo, who really was the all-star of our visit, after the game). But it took several rounds of ice cream and drinks throughout the game to keep my kids from melting. Even if you're used to the sun/heat, it can be brutal through the afternoon.
https://www.mlb.com/redsox/spring-training/ballpark/travel