Don't worry about them, You have a much greater risk of getting killed in a car crash than a mountain lion eating you. In fact I bet you have a greater risk of getting hit by lightning.
I've live in Utah and ride trails where I know cougars are in the area. I've never had a problem with them, They are sometimes curious and want to check you out. But usually a shout or scream will send them bounding away. As stated above they are looking for an easy meal not a difficult fight.
We often chase them with dog in the winter months. ( I don't think California and Oregon allow that any more). So we get to see the cats. I know many of the 200lb cougars we chase could easily turn and tear the 60lb dogs to pieces. But they don't they run away and eventually run up tree when they get tired. They are kinda anti confrontational
Fall of 2010, I was elk hunting and saw a cougar slinking around the edge of the meadow, He was circling and I was pretty sure his path would bring him pretty close to us. I was in como gear and had used scent control to hide my human scent from the elk. So I kept an eye out thinking he would stumble upon us. About 30 minutes later I turned around and he had snuck up to about 15-20 yards behind us and was sitting staring at us trying to figure out what we were. He3 knew we were there hiding, But he couldn't figure out what we were and probably couldn't smell us. The guy with me got spooked and jumped up screaming and the cat ran off.
If you fear things, You will never get out and enjoy the world. I think getting to see a cougar in the wild is a great opportunity, And I would not shy away from the chance.
I have very large hands, I wear XXL gloves. This is a pretty good sized tom's paw print
I definitely would never worry about a bobcat.