I play an SG, so pretty similar. I use the bridge pickup the most; especially for leads and for brighter distorted rhythm..typical metal and rock. I use the neck for some darker blues lead and rhythm, but more especially for clean tones; strumming, open chords, melodic leads, that sort of thing. I tend to use the middle position (both) the least, if ever actually. As far as the tone knobs go, I roll it off more often on the neck pup than the bridge...cuz if I'm using the bridge I'm looking for a brighter tone anyway, and almost always leave it maxed. But yeah, you should experiment.

Also, don't forget to use the volume knob as well. Like if you have a really overdriven tone when at 10, rolling it down to 2-3 can give you a nice cleaner tone that can be swelled or increased at will.

As a matter of fact, for an example of both these uses at the same time click my "tunes" in my signature below and listen to just the first 30-45 seconds of the track "Late October". Only the lead is me, but I start with a somewhat clean tone, then when the riff kicks in, full distortion (and should you hear the end of the track, it fades clean again). But they're both the exact same amp/distortion setting...the 1st clean one is on the neck pup with volume rolled down to 3 and a little rolled off on the tone knob, then I kicked it down to the bridge with both volume and tone knobs at 10.

I know you said you only had one knob of each, as mine has separate knobs for each pup (4 in all)...but you could still use them to the same effect.