"Distressed" can mean many things from physical distressing (dents, holes,worn edges, etc.) to finish distressing (blistering, wear-through, glazing, etc.). There is a shop near me that specializes in distressed paint finishes. The book below discussion some of his techniques.

Other than that, knots in pine will bleed through paint. The way to prevent this is to prime with shellac or shellac-based primer (Zinsser B-I-N).

Latex paint is not the best choice for furniture. It tends to block (stick to itself or other things set on it). Better choices are oil-based paint (if you can still get it in your area), or sprayed on tinted lacquer or acrylic.

Here is a link that might be useful: David T. Smith furniture