I would run the drip directly into the tank, not the sump. Mainly because in the event of a power failure you'll buy more time keeping the water quality higher. Also it's more efficient to do it this way...dilution into a large volume of water (tank) as opposed to small (sump) will mean less of your freshly dripped water will go down the drain.
I'd still drip into your home drain even though your on a septic tank. Really is way more fail safe. To me it would seem that adding solid free, nitrate rich water to your septic would actually be beneficial to the septic tank. Probably could ask a professional what their opinion is.
The regulator steps down your house water pressure (40-60 psi) down to 25 psi. That keeps your air line tubing from being blown off. I use a valve before the regulator to control it even more. Drip emitor to fine tune at the tank.