When it comes to finding a fairly good cheap web host there is a number of things to consider.
Price: Of course, the first and most important point is the price: it should be low, but don’t get sucked in by some providers offering super cheap plans. Go with one of the well known cheap web hosts, like Fatcow. This way you can be sure that you are not the victim of some low level start up company. Of course, there are exceptions, but for the most part, new companies are not so well rounded like established ones, I think this is quite obvious. By the way, if I mentioned a solution, I should also recommend a good source of information regarding that, so if you want to learn more, visit this page.
Support: another very important aspect. You should look for a service which includes 24/7 support, if possible live chat.
Reliability: I think you are aware of how important this is. The success of your online work can depend on this, however I see that many times this is underrated.
Features/Tools: The plan that you choose should provide enough disk space and bandwidth to your site. Try to estimate the needed resources if you can, however if you are beginner, you’re probably unable to do this. If this is the case, I suggest you choose one with unlimited bandwidth and disk space. You should also make sure that the tools that you need for your online work are available – blogging tools, site builder, shopping carts, whatever extensions you may need later on.
Also if you are a beginner, I would advise you to look around the providers website in order to find out how easy it is to use the provided platform. Is there a detailed documentation, knowledge base and step-to-step video tutorials.
One more last thing would be hidden fees: a lot value hosts have this. You should do a detailed research to make sure this does not apply to your chosen host, or you can end up paying a lot more than what you originally planned.