This page will be about how to paint over graffiti, which is harder than it looks.
Spray versus Brush
You can either use spray paint or use a can and a brush. The advantage of spray paint is that you can paint more quickly, paint more easily over uneven surfaces, use less paint, and work a whole lot faster. The advantages of a can and brush is that you can get custom colors and even match paint colors precisely.
It comes down to what things you value most.
Flat versus Gloss
As you may know, paint comes in different degrees of shiny-ness. There are terms like flat, eggshell, satin, semi-gloss, and gloss. Most public items (mailboxes, posts, fireboxes, etc) are not flat but have some kind of gloss. Yes, over time, they will lose their gloss and become flat in shine. That makes painting more challenging: do you match the resulting flat color, or the intended shine? I tend to use satin or semi-gloss and I don’t try to use a flat to mimic the faded paint.
Using Spray Paint
Spray paint is hard to use at first. You need to practice to apply the right amount, and apply it evenly. If you don’t believe me, get a can and spread out some newspapers in your driveway and try to do a 1 foot by 1 foot square evenly. You will discover that you have to apply it from at least several inches and keep your hand moving quickly and at a consistent speed. Practice it until you feel like you “get” it. You will improve over time.