The biggest price and biggest job on any addition, at least in my mind, is the foundation. You just can't mark out a square and pour concrete. You'll have to check into your local codes and see what the foundations require. If you have to go to frostline, then you have excavating cost, footer concrete cost, block or concrete wall cost, then the cost to backfill with stone, then pour the floor.
After that, you can usually pick up a flyer from the local lumberyards or one of the Box Stores. If you keep things in 4' increments, and 2' increments, it's not hard to figure up a ballpark price of what the addition is going to cost. If you have room to store items, buy some stuff off of CL, or the local paper, and store it back for when you're ready to build. It would also pay to do that when the price of items go on sale. You can also check places like your local ReStore if you have one.
In figuring up an addition, remember that studs are 16" apart, trusses at 2' apart. Next time you're in Lowes, go into the tool section and pick up a ProjectCalc which is a yellow project calculator. They come in very handy for figuring out roofing, studs, siding, paint and so on. So for instance FPM wants to build a 10' x 20' addition, which equals 40'. Your looking at 31 studs, then add a few more in for your jack studs, cripple studs, and corners. Round it off to 40 studs. Depending on todays prices, maybe $150 for the wall framing, then another $20 for your bottom plate and another $20 for your double top plate. You'll have 10 sheets of OSB for the walls, so if you get it at a good price...$70. So far, you are a tic under $300 to put up three walls. Now instead of going 20' wide for the addition, go 24' wide and use the standard trusses that all the companies keep in stock. I don't know what the stock 24' truss goes for but the last I saw was around $40 each, and going out 10' you will need 6 standard trusses and 1 gable end truss, so you have around $300 in trusses. Now you have $600 for walls and trusses.
Of course, you'll need to figure up sheeting for the roof, shingles, felt paper, so add another $400-$500 for that. So you are looking at $1000 for the addition not counting siding, and not counting foundation and floor.
But like everything, location dictates price. Those were just some ballpark figures from around here, rounded off. Going with a pole style of addition, you may be able to knock some money off. It all depends on your local code, style of shingles, style of roofing, then add all of the other necessities in like wiring, lights, windows, doors, insulation and so on.
For the OP....if you can only build a 3' addition, which really would be a waste of money, when you put on a new roof, would you be allowed to build up, and if so, would it look right with your existing home? If you could go up, then you could get rid of a lot of items on the main floor which would give you a lot of space.
