The author prefers to work with Mozilla Firefox (and the Firebug extension) in the first instance, cross-checking with Safari and Internet Explorer regularly.
A lot of time has gone into making Plone's CSS as cross-browser friendly as possible. It usually makes sense to reuse styles from Plone where possible.
Plone has a special style sheet called IEFixes.css, which is conditionally included in main_template.pt. You may want to re-use or customize this for your own themes, if you need to make Internet Explorer-specific overrides.
If you ever find that floating elements disappear temporarily or permanently in Internet Explorer for no good reason, you may have been stung by the infamous peekaboo bug. Try to use the visualIEFloatFix class from Plone's CSS on the disappearing element, or its parent.