When building a new site in Drupal, unless you've got a large team of developers, one of the first things you're going to want to do is pick a new theme, i.e. a site template. Thanks to the efforts of hundreds of developers from around the world, there are over 170 themes for you to investigate for Drupal 6 (even more if you're stuck with Drupal 5), each one with its own set of traits. For example some use a table-based layout while others use a pure CSS layout, some are single-column designs though most are multi-column, some that have literally tons of slots for you to add content blocks, some with multiple color options, and some that act as just a bare starting point for you to build your own.
Here are a few things to look for when choosing a theme:
When you design a page layout you have two options for positioning the various components - tables or CSS. Tables are the old way of doing the design and are very inflexible, not to mention difficult to manage, so CSS has become the defacto standard since the millennium.
An important benefit of a CSS design is that you can add an alternative CSS file to make your page instantly printable. It's both horrible from a user friendliness standpoint to require people click to a separate page for it to be printable, but I honestly also find it really dumb to require people do some special trick just to print your content rather than just clicking the browser's Print button. It also gives you, as the site developer (or the person hiring the developer) a much easier time to make global changes, e.g. if you want to make your site all green & red for the holidays or if maybe you decide to tweak the layout a small bit every few months to add some variety, it'll be much easier when there's one master CSS file.
While some of the table-based themes might look good, long-term you and your site will be better off with a CSS-based theme.
Multiple Collapsible Block Regions
Drupal allows you to place portions of content / functionality around your page using things it calls "blocks". Many plugins also can add even more blocks available for you to use, e.g. Tagadelic adds a block showing a tag cloud for your site's keywords, and as a developer you can really easily create your own. Blocks are positioned on your site into spaces called "regions", with most themes having a few standard regions - heading, left sidebar, top sidebar and footer.
While some have taken this flexibility and have gone completely nuts, e.g. AD Blueprint which as 44 regions, I tend to look for one with about eight regions - the usual header, footer and two sidebars, then also one above and below the page content body, plus maybe an additional one between the header and body for e.g. highlighting the week's most important content
In today's technologically competent world there's no excuse for sites to not be present valid code. Using the World Wide Web Consortium's HTML validator and CSS validator, every developer needs to ensure their code is tested and compliant with XHTML 1.0 Transitional ("Strict" is better) and has valid CSS code. Further, themes need to be tested to ensure approximately 99% browser compatibility, which means IE6 & IE7, Firefox and Safari 3. Thankfully most theme developers have done their best to stick with this, so your visitors should have a pleasant experience.
Hopefully the above will help you on your way to build the site of your dreams, with the CMS of your dreams :)