Just as a heads up, I can interpret "Intranet" as simply a network with servers on it in which client machines will gather information from each other and from the servers. To put it in better words, clients accessing content on local servers instead of the Internet.
As to what you'll need to know, what you're looking for is something called a Thin Client most likely. These remove dependencies on individual PCs for the user and instead uses a central server, similar to "The Cloud" but not to such an extent to deliver a user the user interface and programs they need to get the job done. It packs all of the resources they may need to get the job done. If you've ever seen something such as Citrix, that is basically what you're looking for. All the user needs is a simple device that allows them to attach a monitor, keyboard, mouse, and maybe speakers and any other devices they may need to use to a small box, which delivers data via an Ethernet (or wireless) network to the central server where the heavy lifting is done and then delivered back to the user.
The thin client environment can run on any operating system, Linux or Windows. It's really a matter of what works for you, what your needs are and how you set it up, not so much with the cost.
The Interface in the sense of a thin client will be the same GUI everyone is used to using on their regular PCs, along with the same programs that you all are probably using now unless you switch anything.
Internet connection? Depends on your needs. Most network traffic to a thin client setup will be to a local server in which case a good network inside of the building is needed. IF it is to a remote server that is probably co-located elsewhere, you obviously need a good connection capable of handing 20 different sessions going on at once. Obviously, to do it right the connection will be business class, and it must be reliable none the less and fast enough to handle the needs of the location. Generally, many businesses have T1 lines which provide enough bandwidth to get the job done in most cases, despite the dated speeds of 1.5Mbps/1.5Mbps.