I would look for a lower-end dedicated box with a respectable hosting control panel software (Plesk would be my recommendation ). If you're not familiar with server administration, you would also definately want to seek management services; if you search this forum you should find plenty of help there.
A VPS could also be a very viable option - it's a Virtual Private Server; basically like you're own server within another server; which tends to be a bit cheaper.
Corey Northcutt | Northcutt Competitive inbound marketing with a hosting industry competency. Social | Content | Optimization | Outreach
I am not worried about the placeholders since it would be very static traffic and those are not cpu intensive.
VPS are Virtual Private Servers. They are sort of the go-between a dedicated server and a virtual account. In simple terms, think of a server as a building. With a Dedicated server, you have the whole building so you decide what you want to do with it. A VPS is like an apartment block where each site would have their own private 4 walls and a roof, each would have a nice slice of the space to do what you want in it. A virtual hosting account is like a dorm room where everyone in it share the same space, you might have a bed and cupboard but there is no partition as far as CPU usage goes.
If you plan to go for a dedicated server, it is not going to be a bad move. Something simple should do the trick. I would believe a Celeron 2.0 or 2.4 can handle it.
Budget would be no more than a couple hundred a month, at most. Don't really want overkill though.
Can anyone suggest a company I could go with?
For that budget you should be able to find even a mid grade managed server easily. I would recommend taking a look at offers on the Dedicated Forums advertising section here. Seeing as many hosts have been posting there regularly as well as many do offer managed services (if the server isn't managed it is usually available as an addon by many companies).
Wish you the best of luck in finding the one right for your sites.