I used to paint a lot of steel, some of it similar to the rusted surface you have that were at one time painted.
What I found that worked best was to mechanically remove the rust with a wire wheel, then treat the remaining surface rust with a phosphoric acid based conditioner. Lately, I've been using water softener cleaner or dehumidifier cleaner because it's cheaper than the commercial products and nearly as effective. After the surface is rinsed and dried, I apply the best steel primer I have around. Today, that would be Sherwin-Williams DTM Industrial primer. Finish coat is usually an enamel, the epoxies or urethanes are the most durable.
Most of the rust in your pictures looks like light surface rust. I'd be tempted to try the conditioner, first, it may remove most of what you have. If not, you can go back with a wire brush or wheel and get the reamining heavy stuff.
Some of the specialty coatings like POR-15, are really good for frames and undercarriage. The durability can be outstanding.
