If you don't want to spend a lot of money on web hosting, shared hosting is the way to go. This form of cheap web hosting places your website on a server with other sites. So, yes, your site literally shares server resources with others, hence the tier's name. This means that it's far from the most powerful web hosting type, however. The sites sharing the server compete for resources—everything from throughput to storage space. You'll want dedicated or virtual private server (VPS) hosting for muscle if you expect big traffic, or if you want to insulate yourself from big traffic spikes.
If you want the security and privacy features of the above solutions while not paying too much, Rackspace offers the best alternative. In fact, they claim “256-bit Encryption in transit and at rest.” Rackspace offers a basic plan at $2/user/month, with huge 25 GB mailboxes, 30 GB cloud storage and unlimited email aliases. You can run your emails from Apple Mail, Mozilla Thunderbird and Microsoft Outlook.
A dedicated server will likely cost you more than $100 per month; it's definitely not cheap web hosting. The benefit? Your website lives on a server all by its lonesome, so it takes advantage of the server's full resources. You'll probably need to handle firewalls, updates, and maintenance yourself, however, unless you opt for a managed server, which costs even more money.