Category Organization and Calendar

Hello everyone,

I had an idea for a site, and I wanted to start with WordPress to see if I could piece it together in WP proper or at least bastardize it with plugins and custom code until I got what I wanted. Briefly, I want to create a central site for my city to find events going on around town. From the tech side, I was hoping to have 3 basic categories:

Artists – I figured this would be a static Page that would show a bio, genre tags, and any upcoming events if there were any.
Venues – I was thinking this would be a Page, listing static information about the venue (Contact Info, etc), as well as show all the upcoming events at this venue.
Events – I thought these might be Posts that I could categorize using tags or something that would associate with them with:

1. An Artist
2. A Venue
3. A Date

In the case of the latter, I was also hoping to find a calendar widget or something that would help organize a lot events by date with a smaller widget that would easily let the user navigate to an event date (instead of the post date that seems to be what most calendar widgets are set to show).

Finally, I was hoping to make it easy to filter so that if someone wanted to see what Comedy events were happening on Saturday or if there were any shows at the XYZ Pub, they could filter and find that information quickly?

So far, I’m way out of my depth on my current installation. I’ve put categories in the menu and it’s not even showing posts I put in those categories, so I’m kind of lost. I’ve used WordPress as a blogging platform before and loved it, but I was wondering if there was a way to repurpose the categories and tags to achieve what I’m looking for here. Thanks in advance to any advice pointing me in the right direction.