well if you have some experience in those other languages i think you will find php and mysql easy. imo the documentation for php is excellent.
personally i would recomend a nix platform. windows has its place but imo the majority of people will be best off using a nix variant. i dont think you not being familiar w/ unix will be much of a hinderance to you. if your familiar w/ programing that at least tells me your brain works and the few things you might need to learn should be easy. familiarize yourself w/ *nix file permissions and that maybe all you need to know.
if you went w/ a dedicated server and didnt want to pay them to manage it for you, then you would need to be much more familiar w/ *nix though.
youll need to do some homework on hosting to see who offers what you need. ive been very happy with lunarpages.com, support has been excellent as well as the quality of the hosting service/server performance, and im fairly picky about hosting(ive prob tried at least 10 diff hosts). i dont know about the sox binary but they meet everything else you listed. they also run suphp which has some security benefits. they run the latest version of php4
one thing i really like about their setup is you can have your own php.ini file, so you can adjust settings to exactly what you need.
i would not recomend dreamweaver for anything but rapid html development, espescially if you know how to code by hand. but dreamweaver IS a nice html editor... of course the highest quality html is produced by hand still.
you need to understand the scripting your doing, so i see no sense in letting some ide do it for you. the php code dreamweaver produces is ugly ugly ugly.... definately consider dreamweaver for html, but be aware theres other capable(and free) choices.
i would install php and apache on your local machine and develop there. i prefer to do it this way because it makes development very fast. some prefer to develop on the actual server, and there are benefits to that but i prefer to develop locally, and then just test thoruoghly when i upload it to the real server. to me, having to upload via ftp for every tiny change while im coding is totally out of the question. holding controll s to save is way to go imo 🙂
if you decide to develop locally, try to use a similar version of php as what the server is running, or just be aware of any differences between your version of php and the servers.
make sure to get a code editor w/ good syntax highlighting abilities. this will make your life much easier. i dont like dreamweavers code editor at all.
theres packages that come w/ php apache mysql etc all ready to go. some of them are just a simple double click on the exe and its all set up on your machine ready to go. one i like is:
http://www.apachefriends.org/en/
but theres other packages like this that may be better, but i havent ever needed or desired to try anything else
as for the quiz script, that shouldnt be very difficult. i would check out hotscripts.com, download a few, look and see/understand how they did it, and then tweak it to your needs.
oh... and get firefox w/ the web developers addition 🙂 you will prob find this addition to be a godsend. theres so many features that are usefull to those building websites, i dont know how i ever did without it. i assure you it will increase your development efficiency when working w/ websites.