I believe the best way to ensure the right size on screen is to try different sizes, on screen, and change accordingly (all browsers have options of overall/text resizing for users with different needs/preferences).
If you are using different fonts and they are going to remain selectable and scaleable in the web site then thy will only be available if they are loaded on the users side.
So you have to turn the fonts to gif, jpeg or png eventually and then it will only change in size according to the resolution of the users screen.
So the size of the type only comes into play once you have created a headline for instance and you want to match other headlines.
It is all just relative since the sight might be viewed on a very large screen or a hand held.
When changing the font size from points to pixels in Preferences > Units, my 10pt font shows as 10px fonts. As far as I understand this is not correct?
When Illustrator uses "pixels" as a unit of measure (which it is not), it is really using points. All of Illustrator's underlying measures are in points (1/72 inch).
I'm not sure what you're struggling with re webpages; but you can code text size in XHTML / CSS as pixels or points or as percentages.