Pre amp to sub hookup, or speaker level?

What kind of inputs and outputs does your sub have? A high level connection uses the speaker wires, a low level connection uses the RCA plugs into your amp. Need some more info for a proper answer.

Is your sub passive or powered? If passive, you MUST provide amplification and run speaker level to it, but don't just bug off the same terminals as your main speakers. You'll need another amp and y-connect the pre to both amps. If powered probably the best way is to run line level to the sub, adjust the crossover/filter appropriately, and return (adjusted) line level to your amp. If this makes no sense, keep posting and we'll get into more detail.

my sub is powered. It has both speaker level and line level. My question remains. Is it ok to run a second set of wires off my main amp, or should I split the signal from the pre?
I thought my question was clear, apologize if it wasn't

If you have stereo inputs and outputs on the sub, then do what I do. Simply run your main output to the sub input, then run the sub output to your main amp input. This will give you extra dynamic range.

Ptm,
The direct answer is don't do either. You want to daisy-chain the sub between your speakers and amp or between the pre and amp. That way you use the sub's crossover and filters to strip the (low) frequencies you want it to produce and pass the remaining (high) to the speakers. Otherwise, they both get a redundant full-range signal.

If I have an inferior quality sub, am I degrading the signal by passing it through the sub on its way to the amp? My subwoofer is the lowest quality component in my system.Thanks for the help

Try not to use the high pass filter of your sub.
The method I prefer is to connect your pre-amp out to your sub (line level), use a Y splitter at the pre-amp out and use a ACI line level filter (two version 65hz or 85hz) going to your amp.
In my experience the ACI line level filters are very transparent and your amp is relieved of driving the bass.