Hi Avatar!
Many free hosting sites will foist advertising onto your visitors, usually by way of pop-up advertisements. Although many of these can be routinely blocked bypop-up blockers these days, that still misses the point. Some can get round pop-up blockers anyway.
Check to see whether your own ISP offers an amount of free hosting space. That's the first place to start.
I struck that one lucky because for me, some time after I set mine up, they changed the way it works such that newser sites are framed in a frameset of ugly advertising. Not only do they mess with the look and feel of the site, but the use of frames makes it harder for search engines to spider (so you don't get many results in Google).
I would go for a host that allows at least some server-side scripting, especially SSIs (Server-Side Includes). This would allow you to re-use code for your headers and footers, for example, even if you're not wanting to use a database.
If you know HTML, I'd recommend building the pages yourself rather than using a tool such as FrontPage or FrontPage Express, the reason being that those tools tend to generate huge, bloated, often proprietary code that is unreadable and browser-specific. I've seen sites fail to render on other browsers than Internet Explorer because of this.
Unfortunately, you get what you pay for. If you don't may anything, don't expect much (in terms of space, capability, and freedom from insidious advertising).
I know this is overkill, but I've used
34sp.com, and I've been pretty pleased with the service. It's a paid solution offering the following for £17.95 per year (you'll have to pay a domain name registration fee as well).
If you don't know what eschatology is then don't worry; it's not the end of the world.