Hi,
If you have a web interface, you don't need to install anything on your PC.
However, if you are thinking about making changes to actual code etc, then it would be best to try to copy the hosts environment as much as possible.
To this end, I would check out the server information (phpinfo), then download the software similar to what is on your host.
I would imagine that your host are on a *nix box, so unless you are lucky, you are probably on windows. However, they will probably be running apache that runs fine on windows too (though obviously a few differences).
The version of mysql shouldn't matter too much, but that information is on the info page as well.
If you are going to test on you own machine then you do need a server - I would avoid IIS / PWS for the reasons stated above.
Hope this helps. Need more, let me know.
Jamie