Insulation, Radiant and Vapor Barriers - Uninsulated Walls Blow-in or Batts?

I have a 1940's home with no insulation in the exterior walls. I have found that the living and dining room is particularly cold as it's on the Northwest side of the house (the one that receives the most wind).

My plan is to add insulation in just that room as the other rooms in the house are bearable. My question is should I consider blow in insulation by punching holes in between each stud, OR replace the plaster with dry wall and put up traditional bats. What would be the cheaper solution considering I already repaired and painted those walls last summer?

The house is only 1100 sq ft and I go through 3 tanks of oil a winter.

CELLULOSE!!!!!! If you do batts you'll have to tear out all your drywall/plaster. I used cellulose. I have old wood siding in my 1940s 2 story, so I took off a section of siding, drilled 1 7/8" holes in each studded section and filled up the cavity! If you can do this, this is very easy. If you have traditional vinyl siding this might be more difficult/impossible. I rented the machine from lowes and bought 40 bags and took around 5 back. You can do this by drilling holes on the inside of your house which would suck but wouldn't be as bad as tearing all the plaster/drywall out. Which is better, well I feel fiberglass does do a better job, but when you can't put fiberglass down then cellulose works great. We noticed our house is even quiter inside now. GOOD LUCK