Yes, a nice mic will make a small difference, but what makes the most difference is the skill with which the mic is used.
You also left out a lot of information.
Will you be shooting primarily indoors or outdoors?
Do you already have the accessories needed for the mic (headphones, boom-pole, shock-mount, wind protection)?
Which audio recorder do you have?
What other audio gear do you already have?
Who will be "swinging" the boom?
Do you have a PSM? - if no, who will be monitoring the audio?
How much experience with production sound do you, the boom-op and the PSM have?
How are you handling the audio post?
BTW, make sure that you scout locations not just on how they look, but on how they sound. Sure, that alley may look great, but if it's 100 yards from a major highway, half a mile from an airport, and half a block from a bikers bar...
Solid production sound
IS NOT just about the gear. A very experienced boom-op and PSM can make prosumer gear sound great, but handing even a $2,000 Schoeps shotgun to whichever PA isn't busy is still going to yield crappy sound. And if you are considering mounting the mic on the camera you may as well give up on decent sound right now.
If you really must have a recommendation right now, the Rode NTG-3 is a great mic for the price.
http://www.bhphotovideo.com/c/product/563798-REG/Rode_NTG_3_NTG_3_Precision_RF_Biased_Shotgun.html