*Reputation - are they well known, have they had security breaches or reports of poor support, do they adhere to certain principles inline with that of your organisation - such as data privacy or protection of human rights defenders.
*Specialisation - do they work in the field of human rights, software applications or general hosting
*Is mail provided - for many organisation it is not an option to run their own mail server, however, is they do not wish to sue a free service such as [https://riseup.net Riseup] or [https://gmail.com gmail], or if they wish to have domain specific email - such as info@mywebsite.org - then it is worth considering services that provide free email accounts.
*Hardware specifications - does the server fits my needs? For most websites basic servers are enough but websites with high traffic can demand more stable or dedicated hardware.
*Operating systems offered - different operating systems provide different functionality and integration with other applications. They also have different degrees of vulnerability and support.