DO NOT REGISTER DOMAINS HERE!
Choosing your web host is just as important as where you get your domain from. In fact, it can be one of the most critical decisions you make depending on how much traffic you have coming to your store. A crumby web host can really ruin your day.
If you have a busy store and you get a host that does not provide 24 hour phone support 365 days a year, you will pull your hair out when your site goes down and have no one to help you get it back up. I would recommend avoiding hosts with only e-mail support or hosts that only take phone calls during limited business hours. That just doesn’t cut it when your site is broken.
You should expect, and you really need, high levels of service from your hosting company no matter who you get your hosting from or what size your store is. Eventually, something will go wrong and you will need support. It just makes sense to have it as part of your package.
To the best of my knowledge, the web hosts recommended below offer packages that have an option for one primary domain, unlimited sub-domains, unlimited e-mails, unlimited storage, and unlimited bandwidth (with certain restrictions). This is the option I use and it has been invaluable to me since I set up many websites. If you only set up one website, there are less expensive options that you might consider, but they are very limited.
There are really only two hosts that I feel comfortable recommending and they are BlueHost and HostGator. I have had great success with my BlueHost account (many subdomains) and can recommend them highly. I do not currently have any accounts with HostGator, but they routinely come up as the other “best” web host for PrestaShop stores.
You may notice I don’t have GoDaddy listed. The reason I didn’t list them as a recommended host is because I’ve seen too many complaints about them and they appear to be a bit glitchy with Prestashop. I know lots of people use GoDaddy, but I think there are better options for a PrestaShop store.