What I want in a hosting service is primarily that it be ad-free and CHEAP. My website has hardly any images on it, so it hardly uses any disk space or throughput at all. I can use any extremely low-end web host, as long as it doesn't have ads.
(Please do not suggest paying my current web host more money to make them remove the ads. If they deserved a single cent of my money, they would have at least given me some actual noticeable large-print warning ahead of time before they put ads on my site. They've also engaged in some extremely sneaky billing practices in the past which had made me start thinking about looking for a new web host even before they pulled this latest stunt.)