Your best bet would be to run with another runner.
Pro/Con on pepper spray: The pro is that it's light and you can carry it in your hand with a handgrip holster or on your waistband with a clip. The cons are that there is no way of being positive that the canister has sufficient pressure to work and if you miss the face, you won't stop the attacker. If you don't practice turning it on and spraying it, it can be difficult to turn it on... especially in a life-threatening situation. Pepper spray won't stop some people.
Guns: You know very little about guns, right? You'll need to get a HCP/CCW permit, or whatever they call it in your state to legally carry a handgun. You'll have to attend an HCP training class and pay a fee to the state for an HCP license. I would STRONGLY suggest that you attend a women's or beginners self-defense with firearms class. You can find where these classes are held by visiting your local gun store. Many parks prohibit concealed carry, so you need to find out what the laws are on your trails.
The Glock 43 is too heavy for carrying while running and the trigger is a little too easy to pull. I would suggest the Ruger LCP or the LCP 2. Both are less than $300 and less than 11 ounces. You should carry in a waist belt with a sweat proof pouch that has either a velcro or snap fastener for quick access and to keep it from bouncing. The LCP and LCP 2 are so small you could probably adapt most water bottle waist belts to carry it. If you choose the LCP 2 with the light trigger, you should get a Kydex trigger guard/shield to cover the trigger to prevent it from snagging on anything and inadvertently firing. (It comes off automatically when you draw the gun.) The LCP has a harder to pull trigger and is less likely to fire in this situation.
If I ever felt the need to carry while running, I'd carry my older KelTec PT-AT. (The Ruger LCP is basically a clone of the KelTec, but the Ruger is made better so since you're starting from scratch, the Ruger would be a better choice for you.
You will, of course, need to practice shooting, cleaning, loading, and storing the handgun when not being carried. Cleaning will be important because you're going to get some sweat on the gun and that will corrode the metal parts.
For home safety, you want a safe like the First Alert 5400DF and bolt it to a bedside table. To open, in complete darkness, you put your hand in the handprint mold and press a code (like middle finger three times). Don't let your kids know the code, obviously. NEVER leave your handgun laying around, even for a minute.