Does it matter share host or cloud host?

The definitions of hosting have really changed over the years. But bottom line your choice is going to be between Shared hosting and VPS.
Unless you are immediately going to have thousands of concurrent users, shared hosting with a reputable hosting company is fine to start with.
Any host that offers PHP is going to be compatible with codeigniter. Look for PHP 5.6 . At this point they should also offer PHP 7.
This thread has some info, a bunch of people recommended Known Host.
http://forum.codeigniter.com/thread-64258.html
this website has hosting reviews
http://www.webhostingtalk.com