What is it that you have - A 'dry well'? Or a sump pit where a pump SHOULD be? And this drain line - Is it a 'gravity line', or is it a line that should be 'hooked up' to a sump pump? Oh, and what 'main line' are you referring to: the drain line, a sewer line, or the main water line???
Now, assuming the pit is simply a dirt hole with an over-flow pipe ... This is known as a dry well. It sounds like water will 'collect' in the pit and be NATURALLY absorbed, and any EXCESS water that collects will rise UP and OUT of the pit via the drain line. If this is what you have, leave well enough alone.
Mother Nature is working FOR you in this situation. By filling the hole w/QuickCrete, you're defeating that end. If you want a different solution, make the hole big enough to set in a 5-gallon bucket where the top of the bucket is at, essentially, 'ground level' in the basement. Make the hole WIDE enough so there's a few inches all around. LIne the pit w/Landscape Fabric or Filter Fabric. Then fill the base w/a little gravel. Cut some 'weep holes' in the bucket about 1/4" down from the top. Set the bucket in the hole and fill evenly ALL around the bucket. Insert your pump. You now have a dry well w/a sump pump.
The excess water will rise up to the holes in the bucket and fill it enough until the pump comes on to empty it. Yes, every now and then, when you smell mold/mildew, run a few 'loads' of water and bleach into the hole and into the bucket. That's life w/a sump pump.
RE: Home ownership being over-rated - Not at all. It's a WONDERFUL position to be in. I do have this unsolicited advice: The next home you want to buy, be SURE to ask your Home Inspector what that 'thing' is and how it works and what problems are assoiciated w/it. Well, maybe by then, you'll have a lot more answers than you do now.