is that, unless your company is a fairly large one, and has the financial and technical resources to run a web server 24 hours a day, 365 days a year, it's not a great idea.
Some companies do run their own web-servers, I have several clients who do it, but they usually do it for specialised reasons - if they are financial institutions, for instance, or have huge traffic loads, or they're running very big and very busy e-commerce operations. Otherwise it's probably best to run a commercial web site with a professional hosting company. Thousands of companies do it.
I host sites for most of my client companies, and I provide all of them with their own email server. I suggest that you consider such an arrangement for your company - you'll have none of the technical concerns, and your site and email will function perfectly. It will almost certainly be less expensive as well.
I'm sure that other forum members will provide you with the names of suitable hosting companies.