Comment A list! (Score 1) 480
This sounds like a tall order. I'd be scared. Buying equipment is not going to fix anything. You've got to learn the existing network before you can make educated purchases. From the scope of the network you describe, here are the basic things I think you'll need to learn about.
Learn about routing. Subnets, CIDR, the differenec between a subnet mask and a wildcard, the difference between static routing protocols and dynamic routing protocols. Default routes. Policy based routing. Observe and document the different subnets you see in your network, figure out their purpose. Look at the default gateway of the clients and the servers. Figure out what device that represents. If you have only one subnet, your network is probabbly to flat. I'm guessing you have at least 2 or 3. Make a diagram.
Learn about VLANS. Tagged VLANS (802.1q), Cisco VLAN discovery (if applicable). I prefer Brocade equipment for switching / layer 2. But I digress. What VLANS are in each switch and how do the physical wires correlate? What subnets run on what VLANS? If you have fiber, you have another heap of things to learn about.
Learn how to make an ethernet cable.
Learn about firewalls. iptables (if Linux), ASA / PIX if Cisco etc.. Learn the difference between access-lists and statefull firewalls.
Learn how to add rules to whatever firewall you use. What networks route where and what firewalls are between the networks?
What are the single points of failure? Learn to deal with those single points of failure. What are the entry points? What software is everything running?
What are the link speeds, where does traffic go, aggregate and split up?
Gather all the contract information for your equipment. Make a printed list of numbers for who to call about what. Seek consultation to fill any uncovered gaps.
Look into graphing software with auto discover. PRTG is wonderful and not that expensive.
In my experience, things don't usually break. When they do it's because:
A.) Someone touched something.
B.) The power went out.
C.) Someone touched something they were not supposed to.
D. ) You ran out of capacity (in a hard drive, on a link.)
E.) A server got overwhelmed.
Lastly, make sure everyone does their Windows updates
1.) If it's not broke, don't fix it. Why does this network need "rebuilt?" What's not working?
2.) Make sure you can put it back exactally how you found it before trying anything.
3.) Never, ever, make a change at the end of the day, or on a Friday. Come in early, real early, for big stuff.
4.) Listen to your users. If they say somethings different, it probabbly is. Take everything seriously.