With a ADSL Modem/router all you are required to do is get int oteh configuaration settings which coud either be:
but you should read your documentation which will tell you what it is. Put in the admin login and password (read documentation) for the netgear router and whilst in the setup put in your aol password and login. You should then have access to the internet.
ADSL is a little different to what I have as I am with Telewest Blueyonder which uses a different configuration. But from setting up a relatives network I recall thats what I had done.
I'm sure someone with more experience with ADSL will able to respond to this thread.
You won't need the boradband adaptor AOL gave you after. The filter may come useful to plug into your phoneline, but one should have came with the router.