Excellent idea. Been using that type of system for years. Have one 1100 gal tank buried above the garden. Wish I had two. It's connected to all the house and out buildings' down spouts so it fills up pretty fast in moderate rain. Keep the drain field intact for overflow and recharging groundwater. I have a 1/2 hp spa pump mounted on a platform above the tank and the intake footvalve suspended a couple of inches above the bottom. A buried black plastic line carries the water down to the main hydrant. Have all the waterpressure and GPM I need. Make sure your septic suckers get it as clean as they can, then after the tank fills up with rain water pump it out on a unused part of the garden and rototill it in. Do this a couple of times and the water you collected will be good for ground application. I never water the foliage. I also have a fresh water hydrant at the pump
to fill sprayers and to prime the pump if the footvalve leaks. In the fall the pump plug is pulled to drain and the main hydrant is opened to prevent freeze damage.
Make sure all your wiring for the pump is run through a GFI device.
Good luck

If it's a plastic tank, you could probably flush it out pretty well, but if it's an old concrete one, wouldn't it be quite porous, a breeding ground for bacteria? How would you get that really clean, soak it with bleach? Would that be good enough?

Sue