Congratulations on your job!
If I were the only person there responsible for the network, my approach would be something like the following. You may however be working with someone else so you might have to fit in around their ideas, or there might be expectations already defined by the company or management. Ask questions and find out!
Anyway, on with the suggestions:
1) Audit the network. Do they have existing network drawings? Written documentation? If not, have a walk round and make your own. If they do, is it comprehensive (you're a newcomer, does it help you enough? If not, how could you improve it)
2) Ensure resilience. Basically, is everything taken care of that you would need if you had to fix a problem? Are the configs of the network devices copied off and secured somewhere? Do you have a full asset list including all the details you would need to invoke third-party maintenance etc? Is there any kit you're unfamailiar with and need to read up on (before it happens)? Do you have spares? Another angle here is security. What are your biggest threats? How 'tight' is your user population? Are you open to the Internet? Do you have a security policy in place? Are the firewall rules etc sensible and adequate? You might even (once you've got everything else sorted and have a little time) want to do some penetration testing of your own
3) Monitor. From your knowledge of the network (should be detailed by now), what are the most logical things to monitor (important WAN links, key servers, anything crucial to the operation). Do they monitor them? If so, evaluate and improve. If not, figure out how you can do it and start. The aim is to collect stats week on week, month on month, that show you normal operation and will also highlight trends and areas where action needs taking before congestion occurs. When you begin to go to your boss each month and report on these things they will see the value of what you're doing.
Should keep you busy for a while...
