If I'm not mistaken, Joomla is installable via Fantastico, which is offered by most cPanel hosting companies. I've installed Joomla on many hosts and it works quite well. If you are going to be putting this on a shared server, I would recommend using either Hawk Host or HostGator. Both companies are reputable around WHT and I have had multiple domains with them. I was with Hawk Host for a month or two and I loved the service; I never had to request support because there was never any downtime. With HostGator, I rarely experienced any problems but when I did they fixed things pretty fast and were very effective in their live chats and support tickets.
You said nothing aboiut your budget or requirements for space and bandwith, so I presume all these are realistic.
I host 2 sites (talonai.com & monetos.net) with Downtownhost.com, 1 site is Joomla and other - Typo3 based. They function normally, support is good (for details you may look at my review of DTH).
If I'm not mistaken, Joomla is installable via Fantastico, which is offered by most cPanel hosting companies.
That is correct, if a host is offering Fantastico (or even another auto-installer) you could install Joomla with just a few clicks.
But even if a hosting provider does not provide you with an auto-installer most hosts do offer the requirements you need to install Joomla.
Remember that with any application you install, you also need to keep it updated, one thing is certain, not keeping your site up to date will result in hacks, no matter if its Joomla or any other application.
There are also companies who offer services to keep your (joomla) sites up to date under certain conditions.
Good luck with finding the Joomla host for your needs.
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But isn't it better (safer) to upload manually all the files?
If Fantastico is on top of things with releasing updates then uploading is no safer. So if you're one to update your script the second a new version comes out then uploading yourself makes sense. But if you're a person who realizes weeks later then Fantastico handling the install and updates is fine. Of course at any time even with Fantastico you can get away from it just by updating the script yourself.
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donotgowithoversellinghost.com don;t click because there is not website like this Just do not go wtih oversellers. There are plenty of good web hosts. I would choose a company which says what does it do for Joomla projects. Check whether any web host specializes in providing wide range of services and applications for Joomla.