It depends on what you're looking for out of a host, actually.
We prefer WiredTree because:
* They have excellent up-time
* They're relatively cheap - we pay only about $60/month to run this and another site. We could run many more on our 'server', but we choose not too so that it's not bogged down. Of course, $60/month isn't 'cheap' for everyone, but for running our business, that's fine
* It's a 'managed' VPS, which means we have guaranteed resources (CPU/Ram/Hard drive) as well as complete control over our software (SSH access, can install/do whatever we want) but also can contact their support and have them do anything - upgrade Apache, PHP, install something new, run a security scan. It's like having on-site tech support so we don't have to know that stuff.
I'm not pushing WiredTree, just why we like them so you have some context of what you get with more expense. Having a VPS in general, with the dedicated resources, is what we need at the core though. We've had HostGator servers in the past, and they seem to be slow at random times because you never know what another site on your 'shared' server is doing.
Down the 'shared hosting' route (though these companies all have VPS+ options as well), I'd recommend looking into the following as well:
* SiteGround.com - Known for specializing in Joomla sites
* Rochen.com - Again, known for specializing in Joomla sites
* Arvixe.com
Site5 is a company I've heard of as well, and heard good things, so not ruling them out either. I have not directly used any of these companies though, but they all come recommended from users who we've heard from.
I hope that helps,
Alex