There is a lot more to this than just the server, really.
First, what are you needing the server to do? Are you only needing something for file sharing? Or are you more interested in domain control or application hosting? The role that your server will perform in your business will greatly affect the type of server or servers you are going to have to get to fulfill the job properly.
What type of network connections and network equipment do you have in place? Since you say you have three sites currently, does this mean that you are all connected through a VPN already, or no? If you are wanting all of your offices to have access to your primary site and a single server, then putting in a site-to-site VPN tunnel between all the offices is going to be beneficial.
However, if all you need is a place for each office to save some data instead of the local machine, then you might not want to look at "one server to rule them all." First off, this makes a single point of failure. If the server goes down, then all three of your offices are basically down. Now, this of course also depends on the level of high availability you budget in to implement, as well as the types of roles your server or servers are doing for your business. But basically if all of your employees have business critical data or applications running on the server and it goes down, that's bad news for everyone in every office. The other problem here might be bandwidth. Lets say 10 people per office are trying to pull data and services from the server regularly. That means twenty people in remote offices have to wait for their information requests and network connection to pass however far of a distance from their own office to your main site to the server, which is handling all those other loads and requests, and then pass all the way back to them. All day, for every single action they need to connect to the server. While it is doable, depending upon the types of services you need and tasks you expect to be doing on the server (such as saving large files or application hosting) then it is not going to be efficient at all.
Give us a little more information about your current network configuration and what you need from your server and that might help us in making some recommendations.