As an extract brewer planning to start going all-grain sometime soon, I can't answer from experience. But my plan is to start by buying a cooler to use as a mash tun. You can use a bucket, but without any insulation you'll have a hard time maintaining the 150-158F required for a good mash. I plan to build mine from one of those big job site drink coolers - they're made from food grade plastic and can help to maintain the temperature for an hour.

Any food grade bucket will do, but keep in mind that the plastic will asborb flavors. So don't use a pickle bucket (etc.) unless you want pickle-beer.