[CentOS] yum custom install

I am trying to learn some of the in's and out's of yum, and thanks to the help of many on this forum, things are beginning to make more sense (though I still have a lot more to learn). My initial Centos install was the "minimum". From there I used yum grouplist and yum installgroup.

However, one of the members helped me with using yum to install php-mysql and I just found on this forum php-gd (which I installed). It appears one "just has to know about these packages" or have I missed something?

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?

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?

Todd