What's the best technique for this? I am sure it's using a sprayer, but that would involve more time and money than I would like to spend. Would a brush work just as well?
While I'm thinking about it, will the paint hold to the metal?
Yep, you can use a brush, but make sure you use adequate primer and eliminate the rust beforehand.
If you are talking about galvanized roofing type, you can neutralize the finish with a vinegar wash, then rinse. Let dry and paint.
I've never heard about the vinegar.
It just takes off the finish? Will it do anything for rust?