The specifications of the computer between the internet and the miners has to be fast enough to handle all the communication between both, but other than that, any extra capacity will remain unused by this host computer. A Pentium 4 might be enough if you run a Linux OS, but if you plan on using Windows 7 or higher, it will not be fast enough. Using a Windows version older than Windows 7 is not recommended due to sercurity risks in Windows. A miner (having a referral key / public bitcoin address) is a target on the internet, so I'd recommend having a well protected operating system.
The speed of miners does stack together, so having more miners does mean you get a bigger piece of the pie.
Having antminers with ethernet connections, means you can hook these up to the internet directly without using a host computer that needs to be powered on 24/7. So consider getting more miners with ethernet connections and avoid USB miners, since these do not stack that well. A computer only has a limited amount of USB connections and USB hubs do not offer enough power, unless you invest a lot in special USB hubs, which defeats the point, since you might as well just get a standalone miner with an ethernet connection.
Off topic: Most renting contracts where utilities are included in the price have a 'Fair Use Policy', bitcoin mining definitely goes outside of fair use. Most real estate professionals already have experience with people running secret server centers in office spaces with free electricity, so most contracts include a clause where the fair use of the utilities is described.