I'd say do one of two things: if you don't care about how the paint job looks, do it with a spray can. Sand as much as possible to remove the peeling paint and layers underneath. Wash it well, then clean it with a wax and oil remover made for painting cars. This will assure that your paint job will last.
If you care about how the hood looks, pay to have it done. Unless you have access to a spray booth, or have a detached garage you can use as a spray booth, even your best effort at painting will wind up with dust and bugs embedded in the paint.
Shooting paint in a garage is going to leave you with paint overspray all over the place. If you have an attached garage, the house is going to get the paint overspray, as well as the odor.