When choosing a web host, there are a few factors you should keep in mind in addition to the cost of the hosting service.
The price of hosting has come down steadily over the years, so that excellent hosting packages can now be had for about $5 a month, and sometimes for less if you sign up for a year or more.
But price should not be the only factor you consider when looking for a web host. A web hosting provider may be very cheap, but if they have no uptime guarantees it is a false economy. If surfers or customers can't get to your site 99% of the time, then you lose goodwill, or sales, or perhaps even being indexed or updated by the search engines.
Another factor to consider when choosing your new web hosting provider is the support which is on offer. Look at the page where the hosting service is selling its hosting packages. Do they mention support? Do they offer it by phone or by email? Do they mention response times? Do they have a forum where you can ask presale questions? Even if you don't anticipate it now, you will inevitably have to contact support at some point in the future, often about something critical.
One more factor to look at before you sign up with a new host is the list of features which they offer. Some old fashioned hosts still do not offer basic services like PHP, MySQL, Perl, blogging or forum software, autoresponders, free subdomains, Fantastico, decent statistics, SSH access and so on. If any of these is important to you, check it is offered without further fees before you sign up.
One thing that no host review ever seems to mention is the web interface on offer to maintain your site, add email accounts, check your stats and so on. You will end up using this interface every day, and some hosts still have maintenance systems which are primitive in the extreme. If possible, look at a demo of this before you sign up, particularly for multi site or multi-domain hosting.
Once upon a time the bandwidth and disk space a hosting provider offered were about the only thing customers were concerned about, but now most hosts offer more than adequate provision. If you get to the stage where your shared host's bandwidth is not enough because your site is so successful, you probably need dedicated hosting - but that's another story.