But you still have to overcome the acceleration due to gravity to leave the earths surface surely?
Only by a tiny amount. And you need to consider forces, because acceleration is as a result of force.
F = ma
So for a 85kg person, you need 85 * 9.81 Newtons of force ie 834N So if your rocket motor provides 835N of force, you’ll accelerate upwards, pretty slowly. At 0.011 m/s/s, meaning that after 5 mins of that you’d be going upwards at 3.5m/s or roughly 8mph.
Just going up at 1mph isn’t getting into orbit
Define up!
To get into AN orbit around the earth you need to end up moving in an ellipse or a parabola, which will involve some sideways motion. What happens to you (ie if you fall back down, continue into space, swing around one or more times, end up in a stable elliptical orbit, or a nice circular one) depends on how much sideways and how fast you were going up.