Vaulta, your front wheel is 21" - there is only 1 21" 773, a 80/100x21. Your rear wheel is 18". You have 2 choices here - a 100/100x18 and a 110/100x18.
Yes, I would recommend 110 based on your feedback. Run about 13 psi in the front and 12 psi in the rear.
Heavy duty tubes are recommended. The stock tubes should be tossed out with your old tires. John's MSR recommendation is fine.
Tire size primer - the 1st # is the width, the 2nd # is the sidewall height (expressed as a percentage of the width), and the 3rd # is the diameter.
As both the 100 and the 110 have a 100(%) sidewall height, the 110 will be 20mm (2 x 10mm) taller than the 100. This is why a shorter rider might want to choose a 100. The 110 tire will jack up the back end of your KDX, transferring more weight to the front and possibly changing the rear suspension sag.
What part of FL are you in, and where do you ride?