The best dedicated hosting companies are listed here: http://hostingscorecard.com/DedicatedS-1.html

The best shared hosting companies are listed here: http://hostingscorecard.com/SharedS-1.html

The best VPS companies are listed here:
http://hostingscorecard.com/VpsS-1.html

There are separate pages for budget hosting in each of those categories.

The methodology of how hosts are rated is here: http://hostingscorecard.com/how.html

There are no details in your question, but you say you are not expecting much traffic. I wonder if you have decided on dedicated for the wrong reasons.

Shared hosting on UNIX/Linux is very safe, Your site main user has no access outside of your root. What this means is that you can not see inside other hosted areas and neither can they see into yours.

The same is not true on a Windows shared host. I had to set one up when I did a .NET project, both on the host for the site and the seperate host for the database I could see the name of every other username on the systems. When I showed this to the people who I was doing the contract for they immediately agreed to let me put the project on a Linux server with PHP-Ajax-MySQL, 100% safer.

The next level (after Linux shared hosting) is Virtual dedicated server. This is a VM (Virtual Machine) you get to select your own operating system. Some will offer the shared kernel others will offer your own kernel. Go for your own kernel, then everything in your VDS (virtual dedicated server) is your own. It is entirely private, your own IT can install applications and easily add domains as and when you want them. You get ssh access (secure connection, to maintain the VM, view logs etc. You can also use it to some extent for applications that are not in your public area (where your websites are). For example secure tunnels for office and out of office staff, then share documents and databases. This is not and is unlikely to ever be true VPN. But so near you are likely to not notice the difference.

The next level is the private dedicated server. I know others will disagree with this, so don't take it as the only opinion on this. But I would never use a dedicated physical server, you have great expense, assume $180 per month, but you do not have the main advantages of a server that you own. You are as limited as you would be in the much cheaper shared hosting. You have the advantages of VDS. But you have the limits.

You see you set up the server, or the hosts do for you, then you go in first time, setup your domains, can script the setting up of users, great so far. But then you say, well since this is our own server lets get some applications on there, real java applications. But no, you bought yourself a sever, you did not necessarily buy a comms link. Hosted applications is very expensive in terms of bandwidth. Hosts know this and will choke you. They can not let you take more than your share of the shared bandwidth that the host has to offer.

You will sit there after a time and be wondering what the advantage of a dedicated host actually is. I can tell you, there is no advantage at all. Even a hardware error, a VDS (virtual dedicated server) should there be a hardware problem the mirror server will kick in. If the server you are on is coming to a service time, your VDS can be copied in the same way you copy a file, to another server and you wont notice that anything has changed. You can not do the same with a dedicated server, to mirror you your host would have to ask you for the cost of two machines. Your drives will be raid mirrored, but your server definately is not.

VDS has all of the advantages of dedicated, but it has a long list of extra advantages too. So forget dedicated and instead go for Virtual Dedicated Server. You will save yourself a lot of money too.

The link is to my own favourite host, when I do this work it is the first I recommend (and I only ever reccomend UNIX/Linux). I have not known any downtime for what must be ten years. The range of applications in control panel is good, you can add more, the access for developers is excellent.

The classification as Shared and Dedicated doesn't make nay sense. Rather, an IP address can be either STATIC or DYNAMIC.

A STATIC IP is one that your ISP provides you and that belongs to only you always.

A DYNAMIC IP is one that is allocated to you each time you switch on your router and connect to the internet. If dynamic ip is the case, then your ip address will be different each time when you connect to the internet. Also the dynamic ip once allocated to you is released once you switch off your router and any other person trying to connect to net after that might get that ip address allocated to him.