There are many phosphoric acid-based products on the market. These are the "rust removing/metal etch" products, such as Navel Jelly (old school) and many other products with the same active ingredients. Wire brushing is sometimes necessary. Once removed, two-part epoxy primers are excellent in sealing the bare metal.
That said, if you're more of a hardware store/spray can/rustoleum type of guy (no shame in that) the result will last for many years if you keep the car garaged.
Your rusty areas look pretty mild, and I would feel pretty good about that. An acid product is going to eat into some of the existing paint, so you may want to factor in how much repainting you're planning to do.
Since I have worked with several acid products over the years, that is the direction I would go for my car(s) since I find that pretty known. A mild citric acid solution would do well, too.
Another product I've used many times ($60/gallon) is POR-15 Metal Prep. I like this product because it includes Zinc Phosphate in the formula. After treatment and rinsing, is leaves behind a whiteish (and paintable) zinc coating that inhibits new (surface) rust for many months. I like that, because I can take my time treating the rust, and paint it all at the same time.
That said, if you take your time removing the scaly, crumbly rust, the exposed bare metal may surface rust as you work through the project. But that new rust is very light duty, and a final acid treatment right before paint, is all that is needed to get it bare and ready, again.
Spray rustoleum (rust convertor) products contain a rust dissolver and epoxy primer in one product. While such products may not be textbook perfect and may not hold up well to snow, and salty water, that won't be an issue for many who do not drive in the rain or in snowy climates.
edit: for stuff that isn't a show car, like reddish rusty areas on a motorcycle or japanese scooter, I may treat with POR-15 and just leave it that way, unpainted (like it may have been before) and that white coating ages in time, and it leaves behind a metal with a nice patina.