Think about this - even if you paint it, if something gets spilled on it, paint isn't waterproof - you'll have issues with paint....poly or varnish will give you more protection than paint.
Enamels and other plastic-based paints certainly are water resistant. The very fact that you can't clean these paints from brushes and rollers with water should indicate that much. (You need mineral turpentine to clean things, and do so while they're still wet!). There are plenty of paints available that are just as water resistant as poly or varnish. Ask someone at your local paint shop or hardware for an expert opinion.
If you want to paint and get rid of wood grain, a good sanding job will help you out. Put the time in to do a coarse, medium and then fine sand on the bare wood. Clean well before painting (but don't use cloth that's too wet - you don't want to trap moisture). Follow this up with a good wood sealer and then primer undercoat (there are some undercoats that are also sealers, which can save a coat and some money). Primers help the final coats to stick to the surface, and stop premature paint peeling.
Do another very light sand. You aren't interested in taking layers off here. Merely smoothing out any bumps. A good finishing or orbital sander with a fine sandpaper is recommended. Make sure you let the under coats dry to full strength before sanding. Sanding semi-wet or non-set paint will ruin things.
Follow that up with as many coats of your top-coat as you need. Between coats, do more light sanding, and remember to wipe off any excess dust or grime before painting. And again, give each coat plenty of time to dry. Enamel can take several days to dry to full strength, and is worth the wait if you want a nice finish. Paint often gives a minimum dry time on the side of the tin, which is usually when its tacky enough to paint over. Go by the feel of the paint. If it's still tacky to the touch, wait until it's completely dry.
Remember to do several thin coats instead of fewer thick coats. Paint dries faster at the surface, and if it is too thick, fine bubbles will get trapped below the top surface. The end result is an ugly coat that needs to be sanded back and reapplied.
Good hard enamels can be very scratch and water resistant. I use an 85% gloss "jet black" enamel on my cab, and the result is almost a mirror finish. It's seen plenty of kicks, beer and softdrink spills from rowdy mates and kids, and all it takes is a wipe with a damp cloth and it's all clean again.
