Only really big hosting companies keep all support in-house. The majority of hosting companies have a couple of permanent in-house staff members that handle support during the daytime and use third-party support companies to handle support outside of these hours.
Before you choose a support company, please do your research and look at reviews and comments from people who have used the company before. Companies based in Asia tend to be cheaper than those based in native-English speaking countries, though price is not always an indication of the quality of service you will receive.
You should also check out server management services if you need help administrating your company server.