Hosting requirements:

*NIX(Linux, FreeBSD etc.) hosting

PHP 4.2+

1 MySQL database

GD2 library for image resize and thumbnails creation

CURL library is required for real time shipping calculations

last 2 options usually installed by default.

Recommended Hosting Companies:

100 megs webhosting http://www.100megswebhosting.com/

Dinohost http://dinohost.com/

You can find more hosting companies here