With only 4 devices so far, it really looks like economically it's more reasonable to get rid of the coax network as a whole, and install new UTP cabling for all the devices at once. Otherwise you are facing a task of bridging between two different kinds of networks, thus limiting the choice of hubs/switches you can use. Anyway, if you decide to go bridging, buy a hub with both interfaces, coax and RJ45. Your network will be connected to the coax port (actually, your hub is going to be attached to this network as any other device). The new computer will be attached to one of the hub's RJ45 ports.
Dmitri Abaimov, RCDD