If you're going to use the 2nd floor for a home office, exercise room, play room for the kids, mother in-law apartment or any style room where you will be accessing it daily, then you want a full staircase.
Room additions attached to your home will start around $200.00 per square foot finished. A 12x24 room addition = 288 square feet @ $200.00 per square foot = $57,600.00
A 12x24 garage attic room unfinished @ $26.00 per square foot = $7,500.00. You can finish the space yourself for a lot less than a remodeling contractor could saving you tens of thousands over the attached room addition.
You may not need the living space yet but want the additional storage a attic truss provides then a staircase still is a great idea. The staircase does cost more but down the road you'll be glad you did.
In conclusion, a staircase is a better option in most situations.