Trying to sync iTunes to work across all devices

iCloud, Home Sharing, iTunes Match, they all do different things.

First of all, in order to use Home Sharing, you need a wifi network. Then all your PCs, Macs and iDevixes that are connected to the same network can stream iTunes content to each other. This might work for your iPad when you are home, but once you leave home, your iPad will have no music. And it's a total non-starter for your Mac at work.

iTunes match might work to get music from your home computer to work, but it is a paid subscription service for $25 a year. It works great if most of your music was bought from iTunes, but if not, it strikes me as a lot of hassle to make sure all your music is matched correctly.

The easiest thing to do, IMO, is to hook up your iPad to your computer and copy the music, either by syncing or manually managing music. Then at work, listen to your music from your iPad. The cloud is useful for many things, but IMO, music still works best when it is stored locally on your device.