All good questions...

Check this site to see how vulnerable the information your boradcasting makes you.
http://www.grc.com/x/ne.dll?rh1dkyd2

The nice thing about the ShieldsUp site is the amount of easy to understand information available.

The ads warning you could be right but you were right not to click them. At least 50% are spyware and why pay for what you can get for free?

Start with ZonAlarm since you are new to the tech that runs the internet. Once you feel more confident go with Sygate Personal Firewall or any other fw that lets you make your own rules.

To honestly answer your question if someone really wants to hack your computer it can be done with or without the IP up front. However broadcasting your IP can allow rank amatures to run scripts against it at will.