There is nothing to be confused, check the hosting site you find, talk to their support and see what type of response you get and according to that choose a host
I think you need to specify all details for the web hosting account you are looking for and then start the search. Your question sounds really general for me and that is really hard to answer it
A good web hosting is a hosting that come with high uptime and reasonable price. Sometime the most expensive web hosting does not mean they are best in web hosting industry. However, I bet you all of cheapest hosting such as $1 monthly are really bad in both quality and support. It is also depend on the type of website you are creating. If your website are common platform such as Wordpress, Joomla, Mambo, Drupal , Typo3 and similar then most of hosting could capable on them. If you are going to use your own customer script then it is another story. If your script has been designed to consume too much resource and make a whole system unstable, such as content scraper script, then you have a high chance to be kicked from most hosting providers even a reputable one. Otherwise you may be forced to upgrade into their dedicated server or VPS instead of use shared hosting, which will cost you a lot more anyway.