Picking a web hosting provider
Picking a web hosting provider is not an easy task, there are many things to consider. I will try to give you a heads-up on what problems you might have with any of the current hosts.
Shared vs virtual-dedicated vs dedicated
A "shared" plan is a hosting plan that puts you on a server with many other users, I would recommend these if you have many suites with small traffic. As soon as you have around 1000 visitors per day you will most probably find that your site is not loading anymore or errors like "Service unavailable", "Too many connections" or similar errors.
Virtual dedicated servers (or VPS)
The server is still split to a few users but you get your own operating system with your own dedicated RAM memory and processor, each user having its own dedicated resource, it is very close to having your own server. These usually have much less storage space than dedicated servers.
For example this might be a server with 16GB of ram and 8 users on that server receive VPS with 2 GB of ram each.
I found VPS to be surprisingly fast and very reliable. It is a great way to separate resources between sites with relative high traffic.
If something goes wrong at hardware level it is more likely to be detected and fixed at provider's end than a dedicated server that is only used by you.
Data should also be safer than on a dedicated server, because it is usually stored in raid mirroring systems or fiber channel storage. On dedicated servers you usually have 1-2 hard drives with no raid, if HDD fails, data is lost.
This means you are getting your own server box in the data center of your provider, your own operating system and all that is realted to the actual computer. This is more expensive than the VPS since the resoruces are not split to multiple users.
No such thing as "unlimited storage, unlimited traffic"
As a general use you should stay away from any hosting plan that says "unlimited space, unlimited traffic", nothing is unlimited and the sooner you know, the better. If a hosting provider is offering you unlimited space and traffic then you can be sure that you will have other limits that will block you as soon as you have some traffic on your sites, things like max apache users, total database connections and similar things will cause your site to show "service unavailable" or similar errors whenever you have a decent amount of traffic. For example a GoDaddy "unlimited" plan reached these hidden limits with under 1000 visitors a day.
I found that most virtual-dedicated servers limit your network connection to around 10mbps (~1.2MB/s) and around 100mbps (~12.5MB/s) for dedicated servers. Normal/shared hosting's plans might be somehwere in between but should most probably be unstable since there are always multiple users on the same server. Before moving many sites on a new host you should buy a plan and do some upload/download testings between different servers.
Note that a fast download from your site to your computer might not mean that the host is fast, where possible test the download speed from different continents too.
Fasts providers that I tested (dedicated and semi-dedicated servers) are: GoDaddy, RackSpace, Amazon AWS.
Being charged for extra traffic
Make sure your host has a way to suspend your plan if you reached your monthly traffic limit, instead of charging you for extra traffic. I found that some hosts like LeaseWeb has no way to suspend your account when you reach your monthly traffic limit, instead they will charge you large amounts of money for extra traffic.
Setup fees and taxes
When you compare the hosting providers, especially for virtual-dedicated and dedicated servers, you will find that the ones with lowest prices also have setup fees or tax will only be shown at checkout, so consider this when you compare prices, try to reach the checkout page to know exactly what you are paying.
Total emails you can send per month, day, etc
Most hosting providers will limit the amount of emails you can send per month and per day, mostly with shared hosting plans. Even worse, some providers like GoDaddy will limit this even with fully dedicated servers, they will force you to send all email trough their mail servers.
Upgrading your plans
If you think your site will expand in futuere and you will need more storage or traffic, make sure this is possible without having to move all your data manually, which might be a pain.