An MLB game is only cheap if you find an excellent promotion or choose the nosebleed seats that I prefer. When I was broke, I bought the best seats and now, financially solvent, the worst seats.
Part of the "experience" is the food; with each park, you have a local twist. At Fenway, it is the lobstah roll washed down with a Sam Adams beer. The remainder is what you would expect at any ballpark, with hot dogs, peanuts, and soda topping the list.
Management has also created an urban garden on their roof to contribute to the food list of available items. Before the game, Jersey Street becomes an entertainment venue for ticket holders with various food and souvenir options, and expect to pay an uptick in prices. No different than a concert, movie, theater production, or an amusement/theme park.
There should be no sticker shock for a Fenway adventure, and taking public transportation or going to the less expensive parking lots within a 20-minute walk is advisable.
The expense is exorbitant, and Fenway is one of the most expensive places to attend a game on the MLB landscape. If you have a limited budget and have children in tow, I suggest a trip to Worcester and the WooSox. Last season, the Boston squad had an inordinate amount of Worcester products surface. Major league dollars for minor league talent, like paying top dollar for Aerosmith, only to see a tribute band show up.
The pricing of food and beverages continues to spiral north rather than south. Inflationary pressures drive the cost, but even without those pressures, the prices move upwards along with the inevitable ticket increases. The food itself is either delightful, passable, or awful. Ranking-wise, it is middle of the pack.
Taking the "T" to Fenway Park has a particular risk assessment. The MBTA is having a wee bit of management difficulties addressing safety concerns. If you enjoy the possibility of a trolley collision, a train fire, a possible door decapitation, and then when the hell is this car moving, go for it. All of that has happened. Good luck, and walk or use Uber or Lyft.
If you limp into Boston from elsewhere, the city is one of the most expensive in the nation. Be prepared to pay accordingly for a hotel and dining. Boston is a great city, and so will your bill for visiting.