That's a very credible first attempt, better than most!
As this is server configuration code it's really important that you understand how it works and what it does. Your hour of research was not at all wasted!
The rules each produce a 302 redirect. Add the [R=301,L] flag to fix this.
Add a new, third, rule for redirecting non-www to www. This domain canonicalisation code is important and widely posted here. This rule will be last in the list.
So, your new rules will be in a specific order. The first rules will process very specific requests, those with /products or /account/admin in. The last rule will be the general catch-all if no other previous rules matched.
Some requests will match none of the rules (such as www requests for the correct URL) and none of the rules will be activated.
Once you have the rules working, it is important that the pages of your site link to the "correct" URL for each page. It is not a good idea for a click on an internal navigation link to then result in a redirect within the site.
Another thing you will need to do is make sure you link to images, scripts and stylesheet files, using href="
/path/file" format with a leading slash. It is the browser that evaluates the full URL for embedded objects. Using the href="../../path/file" linking format usually leads to failure.
[edited by: g1smd at 4:56 pm (utc) on Nov 10, 2010]