we had a coder and our website is now on wordpress.Well since this is a Linux site obviously the way to go about it first develop the web site locally on Linux (preferably slackware ) . until you have things working on localhost there is not much point hosting it live. Its much easier working locally to change code rather than trying to do an edit via cpanel.
Now you say your company wants to "host" their web site but have they got one ready to host ?
So is your company using python or php or asp in its web site.
Now hosting is a bit of a bone of contention ; i've used mainstream and i found them to be totally rubbish.
Now here is the thing let me give you a metaphor if i had a really solid three wheeler car or a jaguar of which the electrics were dodgy it leaks oil and it sounds like the engine is about to cease up , would you choose the "on he surface" swanky jaguar or the 3 wheeler ?
So their is vps ,the cloud but high % uptime, none moody and helpful tech support is important.
So i can;t really be more specific unless your more specific or is the company web site a vision or work in progress then i can give you a few hints. Can you code yourself in anyway?