"So I've just signed up to the RSS feed for another blog and it gave me the option of directing it to my google homepage or something called newsgator"
A RSS feed is really just a special type of web page and you need something to read it.
So your Google homepage could be set up to show it or you can get special apps, which is what I'm guessing newsgator is.
Some browsers can also work with them, Safari for example does and that's the one that shows me how many new stories there are for a web site in my bookmarks bar.
What browser do you use?
"Wordpress offers an RSS widget"
You should be able to use that to either display the RSS feed from your own blog or to display the feed from something else. So if you're a local blogger you might show the RSS feeds from other local blogs somewhere on your page. I don't think you'd want to show your own RSS feed there, but it's possible.
As a general rule your RSS feed is something that other people will consume and will use to be reminded to come to your web site to read the whole story.
I think that Wordpress just give you RSS out of the box with no further tweaking.
This page has some information about it:
codex.wordpress.org/WordPress_Feeds
So it sounds like you can just use:
MyWebSiteAddress/?feed=rss
There are also example on that page of how to show a link for that somewhere on your page.