There are 1000s of hosts to choose from...
The first thing you need to consider is what platform you need, ie. Windows or Unix/Linux. You'd normally go for Unix/Linux unless you have specific requirements that demanded a Windows platform (eg. running ASP or ASP.NET applications). Windows hosting costs more due to Microsoft licensing fees vs. free Linux licenses.
Next you need to think about the resources you need. For example, the amount of bandwidth you're expecting to need (if you're hosting video/large files you're going to be concerned with bandwidth!), amount of disk space required, processor and memory requirements if you're going to be hosting something heavy. Most hosts offer the same features - usually it's just the hard drive space and bandwidth that differs.
From your resource requirements you'll probably also get a idea whether shared, VPS or a dedicated server is the way to go. If you're new to web mastering then a shared host would probably do you fine and you can upgrade as required.
The BIG differentiator (and one of the most important in my opinion) is their support, especially if you're starting out. You have to realise that anyone can claim to be a web host - so people can be part-time web hosts and not be available to help you when your site comes crashing down. This is hard to determine without talking to other webmasters who have experienced their services but there are a number of review sites you can visit.
It's also important to realise that many web hosts pay commissions to people for recommending them - so I a lot of "review sites" will be recommending hosting companies that pay the most commission, not those with the best features and support. Try to find sites which provide user reviews - not just the opinion of one person - e.g.
http://www.webhostingreviews.com/.
You'll always find that some of the bigger hosts have complaints against them - don't worry too much if you find someone with some negative things to say about a host if the majority of people are happy. Some people have totally unrealistic expectations and will complain about anything.
Once you've short listed a couple, then look at the prices and work out which is the best value - but be willing to pay for support - don't sacrifice good support for the sake of a couple of dollars a month, no point having a web site if it's unstable and no one is there to fix any problems.
I've never used them but Hostgator (
http://www.hostgator.com) generally gets lots of praise - and with a coupon (see
http://www.retailmenot.com/view/hostgator.com) you can usually get your first month of hosting at Hostgator for free or 1 cent so you can give them a spin and see whether they are right for you.
If you need any further advice, let me know - happy to help.
