I would recommend implementing your functionality as User Controls, rather than as Web Parts, and building that into the master page.
If you have to use Web Parts, then build those into the Site Templates you're using to create your subsites.
Failing that, you're into the realms of writing a feature to populate the web part zone. That's possible, but can be unreliable if you're also using the publishing features, I've found.
To apply the master page to subsites, I would create a Feature with a Feature Receiver that sets the subsite's master pages. Note:
- Sites actually can have two master
- Meeting sites use a different
master page to other sites
This is for 2007, but the same is true in 2010
I would then use feature stapling to active that feature receiver when the new site is created.