First thing you need to do is figure out what is using your network bandwidth. Without that information all of this is just guesswork.
What I would recommend is to take a PC with two network interfaces and wireshark or TCPdump, depending on Linux / Windows. Set it in between your main switch and router, and then sniff the traffic for awhile. You can do all sorts of stuff with the data. A better solution is to use a network tap, but these maybe outside of your budget.
I've seen organizations with one or two users hogging all of the bandwidth because they watch youtube all day, or listen to internet radio, or download porn.
Find your highest bandwidth users and figure out what you can do about them. Here are some options.
Block their access. i.e. if you can.
Install a caching proxy server for web traffic.
Install QOS guarantees that prioritize some traffic over others.
Cleanup PC's if you find that you have a virus / bot problem.
The correct course of action is Dependant on what you find with the sniffer.
It is important to know what your most business critical data traffic is and prioritize that, this may require meetings with your management before or after using the sniffer. I've seen digital print houses do just fine with this sort of setup, and they were doing a lot of large downloads, but they didn't have anyone sitting there listening to radio or watching youtube all day. Currently you've got about (6MB / 60 ) == 100k per user of available bandwidth. The fact that you've used it all up indicates to me there is something else going on, I'd be most concerned about botnets or youtube or lots of downloads.
Also, I'd strongly suggest deploying something like cacti, or RRDtool on an old PC. Once configured they will give you historical information on your bandwidth usage. There are a lot of really good Open source tools available to help in exactly this sort of scenario, but you'll have to get your hands dirty.
Once you know your data needs, you can start to explore your connectivity options, T1, cable, DSL, etc.