Joneseyt-
Wow how exciting to be adding a new space and value to your home!
So I see that you want to add more insulation to your space, first question I have now is how much insulation do you have now? What level of R value are you seeking to achieve in your new space? Are you pulling a permit for this project? What r value is required in your municipality for attic spaces?
One approach that you can take is to basically frame a new ceiling underneath the existing ceiling. This of course depends on how large the room is and how you will frame the ceiling. If it is extra large and what size framing members you get will determine how you approach the framing.
I would also think that you are going to want to do some lighting in the room and maybe you will want to make this lighting recessed? If you do make sure you remove the drywall in the areas where the cans will go unless there is not any finish materials in there at all right now. Also make sure that you properly ventilate this new space that will be a vaulted ceiling.
I have one other question for you, what is your budget for this insulation project? The reason I ask is because one other alternative to using fiberglass batts ( I cautiously am assuming that this is the type of insulation that your desire to add framing depth to the ceiling derives from). The other alternative to using fiberglass batts is using either a closed or open cell spray in foam insulation. Each of these insulations have their own considerations to take into account and you would have to consult with an insulation contractor who specializes in each one of the types to come on site and take a look at your project and ensure it is feasible. They should know the issues such as load demands and ventilation issues pertaining to your specific situation.
Using a spray foam insulation can gain you specific advantages to fiberglass batts. You can ultimately achieve an r value of 6.0 per inch with the standard 2.0lbs/ cu ft foam. So if you have 2x8 rafters currently you will gain an insulation value of an r43- 44! That is very close to meeting the building requirements r 49 - 60 of zones 5-8 (cold climates such as Minnesota, North Dakota, Wisconsin and Alaska)
So now the cost of a project and that will vary depending on the contractor and the area in which you live. The cost may range between 1.25 - 2.50 per square foot to have installed however you have to consider the cost advantages versus the time and labor it will cost you to frame and insulate the existing space.
There are other considerations to take into account however I hope that this gives you something substantial to ponder. If you have any other questions please do not hesitate to ask here and then let us know how it goes.
If you do decide to consider spray foam most insulation contractors specializing in this type of product should be able to address specific questions regarding ventilation, safety when accommodating recessed lighting vapor barriers etc.
Good Luck and be safe.