what is the fastest a human can travel that is possible and how ? New Horizons went 10 miles per second...?

10 miles per second with respect to what? With near term technology about 100 miles per second might be possible about the time you crashed into Mars, or zipped past Mars. About 50 miles per second is the best likely if you want to make a soft landing on Mars, as you need to decelerate about 1/2 of the trip. In either case the average speed is about 1/2 that much. Still slower if you want to return to Earth.

Possibly we could circle the Sun in half the time, Earth circles the Sun returning to Earth, 6 months after we left, but that would be pointless except to set a speed record. The path could be slightly shorter than the path Earth travels, so perhaps 105,000 miles per hour, briefly. Earth orbits at about 45,000 miles per hour, so that is our speed with respect to something, when we lift off from Earth's surface. A sling shot maneuver at Venus might help a little, but probably not. Sorry it gets complicated.

Speed really isn't the issue; it's the acceleration and deceleration that you have to be concerned with. We sent astronauts to the moon at 25,000 mph - about 7 miles per second, which is purty dang fast; If we were to send guys to Mars, in the interest of saving time and consumables, we'd probably boost their speed to 30,000 - 33,000 mph. (And, it would hinge on the ability to ***decelerate*** once they got to Mars...)

But in both cases - the issue is how many G's the astronaut will need to experience, and for how long. Gradual accleration can net some very high speeds (think about Deep Space One, the Ion-drive probe) - it's acceleration was very slight, but constant. It could attain some very high speeds if it had carried more fuel - but, it would've taken months (or even years) to get to that speed.