Painting a bike frame

Special paint that is baked to make it harden

Don't sand back too much or you will take off the rustproofing. Use a good metal undercoat, then spray with a can of spray paint. It's best not to use a brush.

As per aluminum I once had a Specialized M2 frame which had no paint. It took lots of loving care to keep it looking good but I had it shining like new. Plus it was probably 150g lighter as there was no paint.

I would definately shy away from painting with car spray paint. Several good bike shops can offer re/spray jobs, which arn't exorbitantly expensive. Or you could always try a car body shop.

manufacturers in the factory use two common practices. One is an enamel which goes in an oven to bake it. The other is powder coating.
Both are very hard wearing. There is no way you will get anything near it at home.
Powder coating is the better.

Most manufacturing engineers do both, and auto painters have ovens to bake enamel, but designed for cars, be not as good as an engineers.
Be cheaper than a bike shop which would probably farm it out, with a handling charge. Big ovens and powder coating plant don't come cheap.
It is quick and simple, should not cost much. But depending how much preparation you do, or want them to do. Painting only takes a few minutes, just a quick squirt of paint and hang it in the oven. The cost is in the preparation.
Engineering places would have a sand blaster which is quick, and much kinder to your bike than sand paper, and do a better job. Is more paint friendly.

You won't get a good job at home without specialist equipment to handle hard wearing paints. But if you wish to try, try for a lacquer paint, and many very thin spray coats. The first few won't colour the primer. And as above, the primer is the most important, several thin spray coats. You would avoid touching the frame as the oil, and more specifically the acid on you skin will attack the metal and the paint will drop off fast. Paint shops use gloves if the need to touch the metal.
How long it lasts depends how carefully you care for the bike. Thick coats chip easy.

For alu. clean it up and a few coats of clear lacquer will keep it shinny if you don't want colour.
There are many types of car paints now days. Some are reasonable hard wearing, but you would need a hi pressure gun to use them. And of course a temperature and humidity controlled booth.

Depends how fussy you are and what your bike and the paint job is worth to you. A home job won't be worth your time spent to do it.