Stackoverflow has dealt with a similar question: https://stackoverflow.com/questions/4617303/does-windows-7-have-a-kiosk-mode
You're trying to configure what is generally called "kiosk mode" in Win7.
For the browser, I'm not positive, but I believe the default application dialog first included in WinXP had the option to, along with choosing which application was to be used for specific activities, limit access to other applications of the same type.
However, you can do this relatively simply by installing IE (or FF) and creating user accounts that prevent installing any other apps. Google Chrome, because it usually installs in local user profile folders, may require more lockdown to prevent install.
UPDATE adding link with additional info:
Here's an article regarding setting up Windows 7 for a kiosk-like interface lockdown: http://jaredheinrichs.com/how-to-turn-a-windows-7-pc-into-a-kiosk.html
It includes tips on how to lock down a computer to only allow certain programs to be run by regular users, such as Firefox.exe and iexplore.exe.
UPDATE adding links for windows 7 home limitations:
Microsoft support site suggests replacing the shell command in the registry with internet explorer, a rather brilliant idea. This means that instead of the start menu and taskbar and desktop icons showing up when you turn the computer on or log in, you just get IE and nothing else. CTRL-ALT-DEL could still be run to open the task manager and then run explorer.exe but this page has instructions for remapping CTRL-ALT-DEL so that it no longer functions as the three-finger-salute.
These two options together will go a long way towards what you're looking for, I believe. And coupled with a proper limited user account and a settings lock program such as deep freeze (which I've heard good things about but have never used myself), should create a secure kiosk-like system using just windows 7 home.