15 years ago, I had the same dilemma; the more expensive 416 vs the less expensive me66. I bought the 416, and to this day I still use it and it is one of my favorite mics. I feel, had I bought the me66, I would have upgraded by now. But still, having any mic is better than having no mic.
To answer some of your specific questions:
Will the 416 help you achieve better results? That depends on your skills and if the mic you select is the right mic for the source(s) you are recording. Better quality gear will be more important once your recording skills are honed. A beginner with little to no recording knowledge can spend $10K in gear and might still get results that can't compete with an experienced recordist using a Zoom handheld.
Does the 416 need to be close to the source to capture clean sound? I'm not sure where you got this info from. The 416, like any mic, will require knowledge and understanding of proper mic placement. If you are recording quiet sources, then yes, then any mic will need to be close to the source to minimize background noise. Other sources will require different mic positions. Understanding of mic technique is more important than mic selection.
You will need a windshield with any condenser mic that you hope to use outdoors. I don't find the 416 any worse in wind conditions than other mics I own. But then again, I always have my mics in windshields outdoors.
If you are serious about recording and feel you will be doing it for many years, I always recommend to invest as much money as you can in your mics. It's cheaper than selling a mic later to upgrade. Try to buy your mics on eBay, you can get often get a 416 for a great deal. At the same time, don't go in to debt buying gear, unless you are assured return on that investment (ie; the gear gets you more paying work).