1. Admin Menu Module
Those of you that have themed a site for yourself will know why this is important - if you have a broken theme, without the navigation menu, you are screwed. You can't easily find the administration menu in a broken theme. This is a jQuery plugin that allows you to have a slick looking admin menu bar with dropdowns. Very Naice!
Get it here.
2. Backup and Migrate
You'll need this simply because some of the modules you will install later on will f*ck up your site; what I mean by that is when you install an outdated or unsupported module, and you go to load your module list, it will show a blank page or 404 error. Backing up and migrating saves your current setup on the database, and lets you reload it before any significant changes were made.
Get Backup and Migrate here.
3. Content Creation Kit (CCK)
You're going to want to put content on your website, right? Duh. This is pretty straight forward drupal module that allows you to create dynamic content rich pages. 'Nuff said.
Get CCK here.
4. Path and PathAuto
This is an excellent module that allows you to have your URL's automatically generated for you, ie - I make a site about balloons; I write a page titled "99 Awesome Balloon Tricks" - and I publish; the URL that is automatically generated for me will be http://mybaloonwebsite.com/99-awesome-balloon-tricks. Pretty neat, huh? Also, if you create content types, say, an articles section, you can reroute it so that all your new articles will be filed as /articles/my-article-title. Also, for blogs, you can configure dates, and way more extreme filing systems for all you hardcore users.
Get Path here.
Get Pathauto here.
This module is a super handy support module, it enables plenty of other sweet modules. This module provides no visible purpose to the user, but it's basically just a support module, so deal with it. You need this for a ton of other ones. Can't stress this enough.
Get Token here.
This is it for now, just to get you on your feet in the Drupal world.
Here's to great success!