Keep always in mind your target audience, client needs/requirements, project objectives and of course keep it real (according to your budget/time)
Code/design a site that fits most browsers is not an easy task you will need to use those so called "hacks" to work-around common problems (yes mostly on IE browsers) this is something I personally discourage but I've been there when the target it's mostly IE.
Nowadays you have several options, you can choose to detect what browser its in use to browse your site and trigger an script to recommend an alternative browser that follow better standards (with or w/out showing a legible content) or you can code an alternate entry page for those IE fellas or what (most of the time) I prefer is to gracefully degrade the page and make the user aware about his/her outdated browser and recommend an option.
I have read you're using a CMS to create these sites, most CMS work "fine" on most browsers out of the box still as you pointed some CSS and JavaScript elements doesn't work as you go using more "edgy" techniques.
If you intent to develop more sites allow me to recommend the following sites:
To try how your site looks on several browsers (versions, OSes, JavaScript, Java, etc.) you can use
http://browsershots.org/
Compare your favorite CMS options try
http://www.cmsmatrix.org/
To start learning (x)html, css, php and more you can go to
http://www.w3schools.com/
A good CSS reset style sheet is the Meyer's
http://meyerweb.com/eric/thoughts/2007/05/01/reset-reloaded/
I have to say that this is an starting point to archive consistency across browsers :)
I am sure you may have hear or know these sites they are just tools I use from time to time looking for reference, new knowledge or alternatives I can also recommend several FF extensions like Web Developer Toolbar and FireBug.
I guess it's all for now, hope it helps and wish you happy coding/webdev.