There are a few things to keep in mind when trying to run VuFind in a hosted environment:
1.) The Solr index used for searching may require a lot of memory and disk space (though this varies based on the amount of data you need to make searchable); make sure you get a system powerful enough for this.
2.) Depending on what other systems you need VuFind to interface with, it may be necessary to install a variety of PHP plug-ins and libraries. Make sure your host supports the prerequisites or gives you sufficient permission to install them.
3.) VuFind needs a fairly complex Apache configuration to run. If you don’t have permission to add a new sub-configuration and restart Apache, you may have to convert this to an .htaccess file, which may be somewhat complex.
Perhaps there is someone out there who has successfully done this who can offer further advice. Bottom line: it’s probably possible, but you may have to deviate from the standard install instructions due to restrictions and limitations related to not having full control of the box. Feel free to ask more specific questions here if you try the project and run into obstacles. I won’t guarantee we can solve everything, but we can try!
Another possibility that might offer you greater control and flexibility is a virtual server environment like Amazon S3 – it’s similar to hosting in that you pay a third party for access to resources, but rather than getting a chunk of a pre-configured machine, you instead have the ability to define system specs and get full control over the box as if it were your own server. Several people (including me) have successfully set up VuFind on Amazon S3 as a proof of concept – it’s quite easy since you can just create an Ubuntu instance and install the .deb package. The only downside is that (at least for me) Amazon’s pricing model is a bit confusing – traditional hosting tends to have a more predictable price structure.