When I tune my guitar down (Drop C or lower) it starts to sound kind of crappy. I was wondering if this had to do with the strings I'm using or my pickups? I'm guessing more the former?

What would be a good gauge/type of string to have so that lower tunings sound better? If I'm correct in guessing that that's the issue.
I play drop d and c and I use heavy gauge strings specifically ernie ball not even slinkys, they work great, but if you havent had heavy gauge strings before the truss rod I think needs to be adjusted so that you dont ruin the neck.
Ibanez RG7321
Jackson Randy Rhoads V with Floyd Rose
Peavey Valveking 112
Digitech RP70 Guitar Processor
What you're after is a higher gauge strings for more tension. For drop C use at least 10's for a 25.5" scale and 11's for a 24.5" scale. Brand doesn't really matter imho, so stick with whatever you're using.
i play in drop c and drop c#

I use "Beefy Slinky". which are basically a hybrid set. they are 11's at the top (thinner strings) and 12s at the bottom.

they work really well cos theyre nice n tight at the bottom and still slack enuff at the top for tripple bends etc. plus the sustain from em is coooool

I think theyre actually intended for lower DROP tunings.
Cursed to one day crash and burn because we fly so god damn high.