You can wire brush, scrub pad, grinder with flap disc on the exposed areas and then wipe off dust. I like Ospho (phosphoric acid) straight as a neutralizer; but most rust reforming agents; including rust reform primer, contain phosphoric acid as well and do a decent job. You brush on the Ospho (with a tarp underneath you as it also likes to react with concrete) and let it do its thing interacting with the iron oxide. Then wipe or wash off with a hose and when nice and dry throw on paint.
I have had success on frames with many types of paint but my favorite two are POR-15 (most expensive and requires good prep work - rock hard), or farm implement paint (takes a very long time to cure without hardener mixed in, but chemically cures and is tough as nails.) I prefer farm implement paint due to cost, UV and chemical resistance, ease of application (roller, paint brush), it self levels if you put it on thick, color options, and its ability to be recoated with a light scuff of the base layer. I have done multiple boat trailers, two truck's chassis, utility trailer, and my land cruiser's rear bumper, in farm implement paint.
I really like both the Majic and Rustoleum brands. I use the red oxide farm implement primer on trailers on very roughly sanded bare metal. I use the standard grey farm implement primer on auto applications for no reason other than I haven't heard to use anything different.
My boat trailer gets the worst of it; sitting in direct high altitude Colorado sun all summer and getting dipped in the water about 50 times a year. No sign of any change to the paint after 3 years.