You are not being clear here. You call this space an "addition" but I get the impression that this is not new construction. When was this addition constructed? What type of wiring does it have? What dimension are the walls? What is the exterior cladding?

There are a lot of "bests", and there is no one single answer without examining the variables first.

NOT batts.

batts of insulation are by far the most common way to insulate a wall. Nothing wrong with that.

However, if you want some more specific information about your options:

Where do you live?
How thick are the walls?
Do you have K&T wiring in those walls?
Is there a top and a bottom plate to stop air flow/fireblock?
Are the studs evenly spaced to 16" on center?

Thanks to bill, live wire oak and Springtimehomes. Things moved very quickly. Instead of insulation company, sheetrock company insulated, Cost was the same but sheetrockers did a lot of removing of old plaster, rock, wood and old insulation. Used batts, R-13 in walls and R-30 in ceiling, We do have knob and tube. I brought baffles and they were installed in some places. I think I should have had the insulation company insulate and then had the sheetrockers come in but done is done. House has been in reno mode for a full year and I am done. We will blow the remainder of the attic after we have some of the K & T replaced. Many thanks for your inputs.

If you have knob and tube, you just created a fire hazard! It should have been completely removed before insulating. Seriously, it's only a matter of time. K&T needs air flow in order to not overheat. You need to take this up with your contractor NOW, before your insurance company gets a whiff of this. They very possibly could cancel your insurance based on that information. And, when it does have a problem, and it WILL, they might not pay out on the claim if K&T was involved.

I second LiveWireOak's comment. The K&T has to come out--you cannot put insulation next to it, and your contractor should have known that. If it causes a fire, which is a real possibility (that's why you can't put insulation around it), your insurance company will hang you out to dry. You would then have to sue the contractor and the mess could drag on for years. Get it out now.