A few notes:
first off, plucking does not make hair grow back thicker, coarser or anything. The hair just grows back. I think we expect the hair to grow back coarser, but there's no feedback system at the hair follicle telling it that the hair has been plucked or cut or whatever. It's like the myth about how cutting your hair makes it grow faster. Totally not true.
I'm sure that 99% of it is perception.
Regarding the slow regrowth type stuff:
I use the Noxzema Hair Minimizing Shave Gel. You can get a can at Target for $1.99 (assuming you're in the US) or something like that. It's definitely under $5, and costs the same as regular shave gel. Pretty sure you can get it at pretty much any pharmacy like CVS, too. Sure, it's probably intended for your legs, but before I started laser, I was using it on my face. It works pretty well. You'll notice better/faster results if you use it every day, at least I did.
Again, just my experience, YMMV.
Also, make sure you're off it for at least a few weeks/months before starting laser. I was using it while I was getting laser on my face, at least at first, and I realized that it might be preventing regrowth of hairs that should be getting zapped with the laser. It took a couple weeks, but there was a bit of a growth surge once I stopped using it.