Do a search first mate before hearing some individual reviews. It is always better. Search some forums like namepros. Web hosting talk is another one. By exploring these forums you will be able to short list some host which suits your requirements.
You're pretty much the average web hosting customer in your needs - so just about any host should be able to handle you. You have the option to either look for a traditional shared account or you could even go reseller if you wanted to go that route and maybe organize a little better. The offers section here would be a good place to start.
Oh, you have a great number of sites to host. You know, it is not an easy thing to find the most reliable hosting company which you can deal with. I think that to make the right choice, first of all you should do a comparison research to get a clear picture of the company. I suggest you to check out Serverpoint.com, Hostgator.com and Hostpapa.com.
So, choose the host that suits your needs. They all provide constant and uninterrupted services and support.
Many companies offer their services but only few are really reliable and stable. Among them I'd mention solid services from ahosting.biz, powweb.com and ayksolutions.com.
They have been in the web hosting industry for a long while and their reputation is impeccable.
I think that an shared hosting should suit your needs just fine because your sites are static and don't require lots of resources to run. Go for a shared hosting.