What kind of paint should I use to paint cans?

any self priming paint will do 

You may use acrylic paints to paint cans and many basic painting techniques can be employed on them. Recycle and paint tin cans to use as organizing containers, candle holders, gift containers or holiday decorations. 

Most any paint will work well. But to make it stick good, lightly sand the shin of the cans first to make a good bond. If you paint metal that is galvanized, wipe the metal down with vinegar first or the paint won't stay on long.

For the cans, spray paint works the best. Rustolium is agood brand to paint metal.

Cardboard can be painted with latex or acrylic paint with a brush in a few light coats. You can buy 8 oz tubs of sample paint at Home Depot.

For best results, use Apple Barrel Gloss, FolkArt Enamels, FolkArt Outdoor, or one of Plaid's several multi-surface acrylic paints formulas. Reduce brush marks on the tin surface by using a soft-bristle paintbrush and only light pressure.

If they are metal cans, in particular steel, you do not want to use a latex paint on them.  Use an oil based paint designed for metal surfaces.  Proper surface preparation, then a primer for metal surfaces, then a couple coats of an oil base top coat, gloss paint.  You can find it in paint stores if you ask for it.  If you have a rusty surface and no way to get to bare metal, then there are some speciality paints that will react with the rust to form a paint barrier. Look up POR-15 paint for rusty surfaces.  We have painted rusty cattle guards with it and it holds up well except where the tire traffic eventually will knock the paint off.  But it is as wearable as any other paint, may be better.  Exceptional chemistry. It forms a "glass".

What size? What kind of boxes.  I would use spray paint.  If you have cardboard boxes you may need to spray paint them white first to get a true color 

Depends what they are made of. Acrylic paint normally works on everything.