hw and sw platform recommendations

Fedora, OpenSUSE, or Ubuntu are listed as supportable platforms for Omeka. Any recommendations as to which might be best.

Any hardware to stay away from?

The various Linux distributions are more or less equivalent as far as Omeka's concerned. I'd recommend picking a distro that keeps fairly up-to-date with its packages, particularly for MySQL, PHP, and Apache.

Personally, I'd pick Ubuntu out of the three you listed, but any should be just fine.

As for hardware, everything really depends on the scale of the project you're going to create.