You should be looking for a reliable host. You can find a host with for 1$ a month but the headache it will cost you in the future is far more expensive.
It would help if you can be a little more specific. Do you have your own domain (or will be getting one)? Is this for a 1 page website (school/university project, simple info you're putting up), a new website you're developing, a business/commercial website? The reason I'm asking is because it's going to make a difference in what people suggest. If you're just putting up a single page, some ISP's give you your own web space and you can probably stick it up there. If the page has requirements that are a little higher, you might be able to get away with free web hosting, either ad-supported or otherwise. If you're looking to develop a full-fledged site with your own domain, you'll most certainly be looking at paid professional hosting. If you are looking at professional hosting, then the questions are going to pertain towards what sort of traffic you'll be getting, whether you need php, add-on domains, MySQL, and other common features. The more info you give us about your needs, the more we can help you
I have some leftover space and might be able to host you for free, depending on how much space/bw you need. Also otherwise i can host you very cheap, i am only a reseller and i just dont need all my space that i have. Pm me with your requirements and i will give you a go if you get free or if i can get a cheap price for you.