44t in the front with 22t in the rear should give you a pretty good range for a regular 3 speed. You should have a 1st gear that is good for riding up hills, a 2nd gear good for cruising, and a high gear that might be just right for the weight of the bike.
Increasing the size of the drive (front) sprocket will make it harder to pedal, but will have a faster top speed if you have the leg power. Inversely, making the rear sprocket bigger makes it easier to pedal, but you won't go very fast. So, if you made them both bigger, you wouldn't change the ratio much. Same if you made them both smaller, same gear ratio or close to it.
If you have ridden the bike already and used all three gears, you should have an idea of where you might want changes.
If you want a little higher gearing, go with a 46 tooth drive sprocket. Or for lower gear , a 42t. 36t may be too much. The chain will probably need links added or taken out to fit with different size sprockets.