After a god washing and wiping with mineral spirits, we taped everywhere.

The primer we used is Kilz 2 Latex, from Ace (hardware). Two gallons was plenty to get the job done.
We used a short-nap roller for the roof and the sides (where permitted). Brushes were used otherwise.

Rollers with 2' extensions made rolling the roof (under the deck) possible.

The paint we used was Ace brand Rust Stop Indoor/Outdoor oil-based paint. This is marketed primarily as paint for lawn & farm implements, outdoor furniture, etc.