Whats the best grass seed to use in April for quick general grass growth and coverage on and old neglected but regularly cut lawn?

Annual rye grass seed, (as opposed to perennial rye) will germinate quickly and give you an extremely rapid, lush, green lawn, which will be the envy of the neighborhood. However, it will promptly die in late June. Sowing some long lasting seed varieties along with the annual rye will give you a much better chance of having a lawn that survives the summer. However, the best time to sow grass seeds of any kind in in the fall. (Even annual rye, which will last all winter.)

Good luck

Rye seed germinates fast.