I plan to replace a load bearing wall with two sets of columns and cross beams. Is this a sound replacement for the wall? What pitfalls should I watch for, of course, other than the second floor crashing in on my head.

It probably will. Nobody here should be dumb enough to give you the go ahead. There are many variables and calculations that need to be made on removing bearing walls. You have given no calculations to work with. SORRY!!!

The basic steps in doing this are to create a temporary (but structurally able) wall next to the load bearing wall to hold the load while you tear out the old wall. Then, put your columns in and header/beam.

As previous reply stated, you'll will have to have someone determine what size of posts you need, the span between them, and what size of cross-beam you'll need for the job to be safe.