Bob's advice is really good. Having been down this road myself, cleanout of the ashes is a key concern in your build. Fire bricks you can move aside and shovel out pretty easy. Assuming you are burning clean things (ie, primarily wood and not color magazines and cardboard), a metal fire pit you can dump in the garden and rake in to the dirt (helps the plants, too), or put in the compost pile. Poured concrete is a PITA to clean, and if you don't polish the concrete, it will get grimy pretty fast.
A popular project here is to use the drum of an old/recycled dryer for a fire pit. It's about the right size, readily available to most folks, and completely fireproof. Also radiates heat really well.