Established Proprietary Control Panel:
My first host back in the late nineties didn't have a control panel, basically you uploaded your files and paid with a credit card. My second host had their own control panel, and although it was useful, it lacked many features. When I finally started working with cPanel, I realized what I had been missing. The interface was intuitive and there was a wealth of information about it online. I'm not trying to single out cPanel as the only choice, because there are others just as good, Plesk for one. It's just that it is an important aspect to controlling your site.
Without a doubt a companies support infrastructure should be sound. When you are looking for answers you need to know that with an email someone will be there quickly to help. When I run into questions, my first choice is to look online, if I don't find the answer that I need, I go to the tech guys. It's a little bit embarrassing (actually it's a lot embarrassing) on my end to actually ask someone, but knowing that they are there is reassuring.
Pretty self-explanitory. Where it will affect you the most is if other clients on a shared server are banned for SPAM, or viruses. Because each client shares the same IP address, if they get banned, the IP gets banned and everyone else that shares the IP. A strong commitment to security is important, but if it's too strong a client will be denied some basic services like ssh. In the end, it falls back on the support system that they take measures fix any problems.
There's a lot that can be said about features, whether it's a discussion about how many e-mail accounts you need, to whether you need File Transfer Protocol (ftp) access. That being stated, you don't want to be limited when you need the features. Right now you may only need one e-mail account, but in a years time, you may need 200, and most of us won't know what we will need in the future. More features are always better.
It's sometimes difficult to know how much space you're going to need, my experience is you always need less that what you expect. This is based on the average designer, using standard practices of compressing images, and keeping the account file uncluttered. To give you an example of how much space you may need, a typical personal web site is less than 10MB. A standard business site can range from 10MB to about 100MB.
Freedom to Learn:
An important aspect to maintaining a Web site is the ability to try different things. For example, you may start your personal site as a static Web site, and later decide that you want to have a blog, but you don't know which one would be the best choice. A good host will allow you the ability to create a new database, install the blog, and then configure it. Maybe you want to test several different blogs before you decide. The "blog" in the example could be replaced with a "shopping cart" or "faq system" regardless of what the item is, you need to be able to experiment.