First, handle drainage. If you want to install a sump pump, perimeter drain, or water proof the walls, now is the time to do that. You should also install any plumbing drain lines at this point.
Next, framing. Concrete transmits moisture, so use pressure treated, and a styrofoam underlay that would normally go under the sill plate, to keep the walls dry. With pressure treated wood, you need galvanized nails to avoid a chemical reaction that would eat a normal nail. Make sure the framing is designed for the drywall (16" OC studs, nailing edge in the corners and around the ceiling perimeter). And make sure the walls are positioned/sized for any plumbing or other utility lines. For exterior walls, the thicker the wall (2x6 instead of 2x4) the more insulation you can include.
At this point, utilities go in, including plumbing, electrical, hvac, and communications. I'm a strong believer in conduit for running communications lines (like ethernet, catv, and phone) so that you can upgrade those without opening the walls or running wires all over the floor. Note that with more outlets, you will need more circuits, and copper isn't cheap.
Insulation is done after all the utilities are finished. If you have water proofed the walls, then I don't have much against the standard fiberglass insulation. Actually, I like fiberglass because it's easy to work with as a DIYer, relatively cheap, and replacing a piece or temporarily moving it (e.g. in the attic) is simple. However, with moisture concerns, or if you live in a northern climate with harsh winters, then I'd favor the spray foam. The spray foam has the downside of being difficult (impossible?) to remove, but it functions as a vapor barrier and leaves no cracks that air can get around.
After this, you have drywall, paint, doors and trim, and touch-up paint. I like to paint the walls and trim separately so there's less work on edging.
As for the flooring, you would usually do this before or after the trim. With hardwood, you would often do the flooring first, and then the trim goes up tight against it. With carpeting, you would install your trim 1/2" above the floor and the carpet installers would install the carpet right under that.
OK, first of all it is probably best to not get into a shouting match with the local code officials. No matter how wrong you think they are, you still need their approval. So be sure to stay civil!
Second, the question of which code version should not be up to whim. You can verify what copy of the IRC your state and local city uses by looking it up online. Many states make additional adjustments to the code, and your county or city might as well. All of this is easily verified.
Third, put down the Webster dictionary. Building codes and construction have specific meanings for many words and phrases, and a dictionary will not help you.
But to get back to your question, the answer is in the very code you cited... you just stopped reading too soon:
IRC 2009, Chapter 3
R310.1 Emergency escape and rescue required. Basements and every sleeping room shall have at least one operable emergency and rescue opening. [...] Emergency escape and rescue openings shall open directly into a public way, or to a yard or court that opens to a public way.
So it only counts as an emergency exit if it goes directly outside. It can't go up stairs and then out a door. The side door you already have counts as an emergency exit for the ground floor, but not for the basement.
Unfortunately you have learned that if you do construction in an area of the house you are generally required to bring that portion up-to-code. If you were not doing any work in the basement, it's unlikely that the building officials would care about the exit. But if you touch it, you own it.
Best Answer
You'll have to contact your local building department to be sure, but it's very likely that they'll require a second means of egress. They might also have localized information, on ways others in your area have dealt with the problem. It's not likely that you're the only person in your area that's wanted to add living space to their basement.
Based on this code, as soon as a basement is used for more than housing mechanical equipment, egress is required. Though I think most places allow storage and such, and only get picky when a habitable space is added to the basement.
According to the IRC, habitable spaces include any space used for living, sleeping, eating, or cooking. Non-habitable spaces include bathrooms, toilet rooms, closets, halls, storage and utility spaces, and any similar spaces.
According to Mass.gov, Massachusetts follows International Residential Code 2009 with some amendments. Though it doesn't appear that there are any amendments to the section quoted above.