I was put in your exact position four years ago with the current place I work with. Here's some things I suggest:
1- Make a plan. These things can't be fixed in a day. My boss, the CIO said, "Rome wasn't built in a day." He was right on with that one. It took me three years to get things to where they needed to be. One piece at a time.
2- Make sure you break things up and prioritize them. What is the 'oldest' equipment or the pain points? Is the network holding up? Connectivity is the most important part. Make sure you have your network running well before you mess with other parts of the system or put additional strain on the system.
3- Make sure you have the right people on board. I call this checks and balances. You need to have firepower behind your decisions, especially when it comes to making the budget.
4- Remember the phrase: KISS. Burn it in your mind... It means, keep it simple, stupid. Don't bow to salesman, brochures, 'white papers' or peer pressure. Experience and checks and balances are essential.
And finally, be cautious and move slow. Systems don't all just fall apart at once. Once you're prioritized, gotten the right people on board and have your ducks in a row, things will run smothly. If managment gets in your way, refer back to the checks and balances you set up and force it down their throats. It's kind of sad to say that this is just like playing chess, but when management doesn't trust IT in general, you have to prove yourself. Following the above steps will help.
Good Luck.