The big caveat, if you are planning to use the computer for a while, setting
things up with the idea of upgrading later, is, no, you cannot "upgrade"
from Home Premium to Business, preserving your settings, etc.
You can upgrade from Home Premium to Ultimate, (which is a superset of Home
Premium and Business.)
And, you can upgrade from Home Basic to Home Premium, Business or Ultimate.
"Upgrade" in this case means the ability to do an upgrade installation
preserving all settings, etc., and is not about eligibility for upgrade
pricing. You can pretty much always do a custom (clean) installation, using
an upgrade installation key, no matter which version you started with,
though an upgrade installation key means you have to start out the
installation in a running Windows system.
Home Premium has features not in Business (mostly Media Center stuff) and
vice versa (mostly network stuff), thus the obstacle to upgrade
installations.