I used to be satisfied with BlueHost, but recently their policies have gotten quite poor. MODx used to run okay (not fast, but I didn't know better), but after I began deployment, I got letters stating I was using "too much space" on my UNLIMITED package... WHAT?! The sad part is, I wasn't even using that much space - about 4GB. That's when they began throttling the hell out of my account. Made MODx unusable. Didn't even call or complain. Just gave 'em the boot. Later they sent me an email stating they could not reach my credit card to charge the next year of hosting onto it... at twice as much as I originally was paying. Didn't respond. They email again, telling me they'll give me another year at $5.99.
No thanks, BlueHost. They went down the tubes quite quickly.
There are many shared hosts that run MODx well. But if you want to unleash the full potential of the CMS, have a mid-to-large amount of data or are hosting a professional project, (like all other CMS), you'll want a more professional-friendly host. I didn't even know how fast MODx was until I installed it on a dedicated host, and now I can never go back
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I run a few projects in MODx over Google's App Engine. Couldn't be happier. Funny thing is - I'm able to do much more on App Engine then I was on BlueHost before the throttling kicked in... while still keeping it under Google's limit for free accounts. You can see why budget hosting services are insanely profitable. I've found its easier just to pay more out the gate than to try and develop & deploy, then find out you need to migrate to a different server.
App Engine & Amazon services for MODx all the way. Either that, or find a shared host that doesn't make you sign a year's contract