It appears one "just has to know about these packages" or have I missed something?
Well, if they're dependencies then they'll install automagically, if they're related to a program or two (like php-gd is related to php and gd) then the convention is usually of the a-b or b-a format. The rest is usually a matter of installing entire package groups (yum groupinstall) or knowing the package name (a little black magic - but then you can guess and use "yum info packagename" for info, or even "yum info" for everything)
Once I have an install that I like, can I save off the list of packages and use it the next time I do an install?
yum list installed
or
rpm -qa
Also, when I do a "yum list", I do not see the php-mysql or the php-gd listed. Am I looking at the incorrect list?
"yum list" lists installable packages in the repositories currently enabled.