Depends on the old coating. If it has adhered well, you probably don't need to remove it. If it's flaking off, then get the rest off.
Tip: a wire wheel in an angle grinder works wonders to remove old paint. Wear a dust mask. You can get an angle grinder on sale at Harbor Freight for $15. Buy a knotted wire wheel. Also get a full face shield ($10) and some welding gauntlet gloves ($6)
As athelake said, it's likely galvanized. If you're down to old galvanized, it has probably oxidized enough that primer will adhere. If you remove the old paint, you'll probably shine up the galvanized below it, and you'll need an acid primer.
Tip: you don't need acid primer. Muriatic (swimming pool acid/toilet bowl cleaner) will both oxidize the metal enough to let the primer get a good grip. Simply wear rubber gloves and wipe it on with a rag. Let it bubble for 10min and rinse it off well with water. When the water dries, you'll see the galvanized is no longer shiny, and it feels slightly rough. Primer will stick well.
Originally Posted by Mikerson
Your frame is definitely steel since it’s rusting. You need to remove the old coating and any old rust, then recoat with something.
I just bought Rust Bullet for my project (automotive axles). https://www.rustbullet.com
Haven’t tried it yet, but I have used their main competitor’s stuff, POR-15. It does seem to cure very hard and prevent rust. I wouldn’t recommend POR-15 in this application without a top coat since it’s not UV stable.
I've used POR-15 on 4 raft frames, my raft trailer, a horse trailer, ammo cans, propane tanks, and 4 hockey goals. It's tough stuff. I HIGHLY recommend it for a bonding/penetrating primer. I also agree that it's not a top coat.
Tip: use POR-15 as a primer. You should use a catalyzed paint over it. Use their HardNose paint, or: go to the auto body paint supplier in town and buy a pint of alkyd enamel hardener. It will cost you $30+, but will last over several projects.
Then go to Home Depot or Ace Hardware and buy regular oil paint in the color you like. Also buy a quart of naphtha.
Mix 10 parts paint, 2 parts naphtha, and 1 part hardener. Brush, spray, or roll on (use more or less naphtha if you're spraying, but this is the right ratio for brush/roll. The naphtha lets the brush/rolled paint flow out smooothly, then flashes off to let the paint cure. The hardener makes the oil paint dry to the touch faster, and also catalyzes it harder. I rarely use bomb cans for anything now.
This frame is POR-15 primer, yellow HardNose paint, covered by GlistenPC clear with gold pearl flake. When I redo it, I plan to use a bigger glitter flake, and might try some photochromatic powder in the clear! (disappears when it gets hot)