Equipment

Carry a notepad and pen.

Carry cell phone with charged battery. Know local police and/fire department numbers (not just 911).

Carry a pocket knife. (as tool not weapon; Swiss Army Knife or Leatherman Tool.) One you can take out in public without scaring the folks. Remember they are afraid of everything...they do not carry pocket knives. [I had a woman call us to arrest the mail room clerk because he opened a package with a Swiss Army knife! We explained that up until last year all men carries pocket knives and they are still legal.]

Carry a clean handkerchief (or bandana in a neutral color)

If carrying handcuffs, carry 2 keys in separate locations such as personal key ring and loose in pocket or in wallet.

On grave shift, I used to carry small spool of common black thread to create tell-tales at fence holes etc. in 'no traffic' areas to let me know during my rounds if someone had passed. I liked to so entertain myself before motion detection CCTV made it superfluous.

Carry a small flashlight; the newer LED ones are great, like those by Fenix. Carry this even in day light. Carry extra batteries in your locker, car or bag.

If you carry a gun, ensure it is clean, loaded per policy, that you have extra ammo in magazine(s) or speedloaders. Change out the ammo for new each 6 months-1 year.
Ensure you can in fact draw it smoothly. Check all this before each shift, in private. Don't touch your gun while on duty except in a real emergency. Touching your gun scares the innocent and can get you fired and maybe arrested for Assault.

Same principles apply to baton, pepper spray, folding fighting knife, etc. Don't scare folks just to look macho...you will look like an immature idiot.

In your car or locker, keep extra shoelaces, depending on post-binoculars or pocket scope/monocular, a warm jacket, sweater, gloves and hat that will go appropriately with your uniform, some "Cup of Noodles" or canned beef stew, etc., a rain coat, extra ammo..Extra uniform, socks, underwear....you get the idea. [Perhaps a towel? See Hitchhikers' Guide to the Universe.]

It is your actions, demeanor and appearance that garners respect, not just having weapons. (Although sometimes the weapon is the thing.)

Your mind is your best weapon. Try to act smarter than you look.