Most of the shooting was going to take place in a supermarket. Any tips as to how I should go about shooting it?
Sure. Action plan:
Try to secure permission to shoot so there will be no drama or guerrilla pressures
Go to the store in advance to listen to the sounds all around the place. Will you be able to shoot after hours and have liberties? If so, you can avoid sounds of other people shopping, and unplug anything that makes a sound.
Walk around and try to find the quietest spots, then try to find spots near light sources (you will be using their lights as they are, for authenticity - and the sources in stores are diffused and large overhead). Look for light bars on the sides of cooler case doors, or a ceiling light panel to place the actor under that would allow a backdrop with depth (not framed against wall/shelf)
Correlate these two - the spots that are both quiet and close to a light source with good framing opportunities. Place the actor close to the light source. You can take a friend in advance and preframe all the shots with the cam you will use; this will make the shoot much more pleasant and prevent the unexpected, so you can focus on the acting.
You will want to use a large sensor camera; this will allow you to blur the background to avoid logo complications, and make the shots look cinematic. Shoot at 1/60 shutter speed to sync with the fluorescent lights the store uses (this will avoid rolling sensor band problems galore)
Use a boom pole to get the mic as close as possible to the actor's mouth (just out of the top of the frame). If the background noise will be very low, you should use a hypercardioid (ideally Mkh50 to rent, or an at4053b, audix scx1, or oktava mk012). If there will be a tonne of noise, you can use a good (not bad) shotgun - go with the NTG3 (or rent a CMIT5U or CMIT2U if you can). Its inside, so a simple cheap foam windscreen should do (except for the oktava..) Suspend the mic of your choosing on a Rycote INV7, and run the xlr into a Sound Devices MM-1, and that into a Sony Pcm M10 line-in. That will get you cinema level sound to own on the cheap, or you can run the mic to a rented sound devices recorder, like the 702.