Your going to have to pick and choose where/how you save money.
As already stated, all Red Sox games are already sold out. You can get tickets for any game from places like ace tickets (http://www.aceticket.com/), stubhub.com or ebay. As with any ballpark the better the seats, the more expensive they are - it's just that at Fenway they take that to a whole new level. For example, my brother is a big baseball fan and had never been to Fenway (we grew up in Colorado, I live in Boston), so when he came out here two summers ago I got 7 tickets off stubhub for both families to go - the seats were about a dozen rows below the Dunkin Dugout in the center field bleachers and they cost me $100 each (including all the fee's) - this for a Texas Rangers game in June. Hardly a major opponent or ideal seating.
Also as stated, hotels in Boston proper aren't cheap. There is a Howard Johnson's right next to Fenway park, not sure how inexpensive it is, but also doesn't appear to be very nice from the outside. My recommendation would be the Sheraton in Back Bay, which is an easy walk to the ball park and is in the middle of the best part of Boston. If you stayed here you could take a cab from the airport ($20ish), and walk or ride public transportation - and have a wicked pissa time. But the room will probably cost you over $200/night. There are T stops right there at the Prudential plaza. You don't need a car in Boston.
Other comment - your son is a little young for Fenway. Many of the seats at Fenway have been there since the 1950s or earlier, they are wood, they are small and they are packed together REALLY tight. Also, the rows can be really long, as in 30+ seats between the aisles - and I would never ever put my kid down in Fenway. The concrete is just to gross - 100+ years of beer, soda and peanuts ground into it, not to mention the pigeon poop, rat feces, vomit and other assorted nasty stuff that is bound to be on it. I would see if you can leave your son with Grandma for the weekend, you will all have a better time.
Another tip about Fenway - the seats in right field, the sections with numbers in the 90s, don't face home plate, they face the bullpen. So your either sitting sideways in the seat or your head is turned for 3 hours, which is a pain in the neck - trust me. Best if you can get seats on the left field side.