I wouldn't worry too much about the axles, if anything give it a light coat of a quality grease, like a bearing grease, or the red tacky grease, after you clean them up to suit you. That will last longer than paint, which will get scuffed off on reassembly, and make it easier to go back together.
As far as the frame, when you take it apart, you'll find it has wooden bearings. I have one of those disks, and it came to quite a surprise to me when I took mine apart to replace bolts on one gang, that had loosened up. Mine had been used, but maybe not all that much. The wooden bearings were still in excellent shape for its age. I'll attribute that to the PO, who apparently kept it well greased. Again, use a quality grease. Those are great little disks. Love the fact you can adjust it, from a full cut to work plowed ground, then set it for a finish pass, simply by adjusting the levers.
As for the frame itself, for things like that, I use a knotted cup brush on my 4" angle grinder. DeWalt makes some good one's. One should easily do that frame, plus several more large projects. Once it's buffed off, you'll more than likely have a bit of rust in pits caused by the rust. I highly recommend a product called Ospho Surface Prep.https://www.acehardware.com/departments/home-and-decor/cleaning-and-disinfectants/rust-removers/13867 It converts rust to iron phosphate, basically killing the rust. Brush, it on, and let it cure for 24 hrs. before priming/painting. I started using it 5-6 years ago, when cleaning up some of my old implements, and attachments for my garden tractors. I use it on about anything, including wheel weights etc. for my tractors. I bought a gallon at that time, and doubt I've used a quart out of the gallon. It is as thin as water, so it goes along way. It is an acid, so do wear protective gear. I'm pretty sure a quart is the smallest amount you can buy, but will last you for years on numerous projects. I got mine at the local Ace Hardware, but it's sold other places.
Everything I've used it on, has had no rust reappear, like things like this will do after several years, not getting all of the rust out of those little pitted areas, and a lot of it sets outside.
