If you have access to an airless it will definitely make things easy if you are just looking to paint everything. If you need to rent one you may reconsider, I am not sure the going rate.
It is a fair bit more clean up than just rollers and brushes IMO.
Rolling and brushing really won't be too hard though.
The prep time may take a little bit to mask off or paper over things you don't want overspray on but I love the use of spray. It's easy and it covers well. True, clean up can be more tedious but the time and ease may be worth the trouble.
Based on the photos, it appears that power washing the walls and floor will be needed, to remove as much as possible, any soot, dirt or oil based contamination. Then rent an airless spray rig and shoot the walls to clean things up as you may need.
IMHO, this job is a perfect fit for an airless. We did one three years ago just like this.
1st we Cleared out all the left behind trash. 2nd We blew out the webs and dust with an LP air hose. 3rd We taped plastic sheeting to mask the floor, 4th We sprayed everything with Kilz 2.
Then we pulled up the plastic and enjoyed lunch.
After 4 years the tannic acid in the redwood sheathing is beginning to stain through.