Do you own the server? Is it installed on your computer? That's a different question than the OP which is regarding hosting, as that's generally third party (off your site and you pay monthly or yearly).
We don't usually recommend businesses by name on the forum. Guidelines of what to look for, what you might need, that we do all day long.
Dollar wise you're looking from $100US per year to $100US per month which is entirely based on your NEEDS such as bandwidth, near 100% uptime, tech support 24/7/365, every add on (Perl, PHP, Ruby, and more), Storage for growth, that's how many gigabytes of disk space you need, SSL, certificates, a whole range of other options for ecommerce if that's your direction. You'll need to decide if Shared is all you need, or if Dedicated is required... and once there you might want to decide on what kind of server you need, example, rack or truly dedicated. Whether there is a mail server included, what kind, whether is is open or closed relay.... You might have need of a listserver or webmail.
Look at what you are doing, then decide how much is OUCH! to your budget, then find the best host you can for that dollar amount.
With smaller sites Shared often times makes sense as bandwidth is usually more important than how much you can store and serve on the host. But everything named above has a use and purpose, and only YOU can determine what you need or do not need.
But having said all that, any host that is less than $100US per year is probably little more than a hobby site or beginner site.