Are you looking for Organic/Natural recommendations?

Also just bought a reel mower and now hoping to cut down grass height? Currently its over 2-1/2 inches. Should I use rotary mower first to cut it down to 1 inches, followed by reel mower to 3/4 inches?

NO, and NO. If you do it all at once you will severely scalp your lawn. Lower the cutting height slowly over the course of 7 or more mowing's. Lower your deck in 1/4 inch increments. Im guessing you will have to start with your rotary mower first as I dont think a reel mower will cut to 2.25" height.

A good rule-of-thumb is to remove no more than one-third of the grass height at any one mowing. For example, if you are maintaining your lawn at 2 inches, mow the lawn when it is about 3 inches high. Cutting off more than one-third at one time can stop the roots from growing and would require frequent watering during dry summers to keep the plants alive. Also, following the one-third rule will produce smaller clippings that will disappear quickly by filtering down to the soil surface.

it's bermuda. you can scalp all the way down to the ground with rotary mower and begin using reel mower after that. No big deal. They will recover fast with water and fertilizer.