Most of the hosting industry is based on reselling server space of someone else. If the company you select don't own his space, it could happen that when you need to move to another company for any reason, you depend on their willingness to help you. This actually happened me some years ago when the hosting company with which I was working was very helpful, but was sold and after that, when I needed to move a client to another host, the company don't even replied my emails.
It is very difficult to move a complex site without having root access, but I had to do it. Although I lost many days and it was very painful, the migration even wasn't perfect. Now I own a VPS (and root access to it) and my life is much better. If you are really on a budget and can't afford a VPS, go for a shared host like HostGator, which is a reputable company.
2. Don't let your hosting company own your domain.
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Your domain is your brand on the Internet. Moreover, when you acquire links to your website you get traffic from them to your domain, not to your web host. If you lose your domain, all the traffic that came from those hard earned links are lost in an instant. If the hosting company gives you a domain name for free, make sure that the email of the administrative contact is an email that you control and you have a control panel where you can see the ownership of your domain.
3. Avoid Free Hosting Of Any Kind
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Free hosting is good for your resume or to tell the history of your dog, but when you are starting a business, even a little one, it is very important to have your own domain because if your page is hosted at someone's else domain, when you acquire links to your page, you become dependant on your hosting provider because if later you choose to have your own domain, all the links you got will still be pointing to the hosting provider which will get all the traffic that should have been yours.
4. Seek a Host With Good Support
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It takes many YEARS to fully understand all the issues of the hosting platforms. Even many Internet business experts with 10 years+ in business don't fully understand all the options they have in their control panel. So, if you are a newbie, you could be in big trouble almost all the time if your host doesn't give you manuals, advice or help you to complete technical tasks. Remember that you bought a web host to make money, not to lose your time with technical things.
