Escape Velocity, which directly relates to this and might be useful. In style terms and such, and helps clarify what Escape Velocity actually is, and why Constant low speed is perfectly viable.
Heres a Link if you want to read it, though I will bring up the more related points.
Basically though, Think of a Helicopter, and how it can slowly rise into the air. As it is doing so, it is going to space at a slow speed. The problem is Helicopters work via air, and there is no air in space. However, If we had some way to keep the helicopter going, like say some rocket engines, and kept it going at that same speed, then indeed eventually it will go into space, and it will keep going. There is nothing wrong with this logic, for getting to space that is. The helicopter is accelerating upwards at a rate equal to or greater than gravity's pull downwards, allowing it to go up.
So, why do we do it at high speed. This is related to the explanation of Escape Velocity. Escape velocity of earth is ~11 km per second. This is the minimum speed you need to be traveling to go from earths surface to space where earths gravity is truly negligible. This is important, because if you go any less than that, and have no way to apply any more force to propel yourself away from earth, you will fall back to earth eventually. This would be just like throwing a ball in the air. Eventually, it comes back.
This is where Orbiting comes into play. Orbiting is simply constant freefall, but in a sideways direction at a speed great enough that as you fall to the planet, which is a sphere, the land will curve away at the same speed as you are approaching it. This is best known and shown from Newtons Cannonball animations. The orbiting object is constantly accelerating toward earth, but is also going sideways at such a speed that it misses. Because it is in space and there is almost nothing in space to cause friction, it never slows down the sideways direction, and because the planet is a sphere, the gravity that accelerates you on one side, slows you down on the other, and it all balances out.
So, why do we not just go up at a slow speed to go to space, because all that would happen is eventually we would fall back down. The great speed going up is simply to get up there faster, but is also helpful when it turns some of that up speed into sideways speed, allowing it to smoothly go into orbit. If the helicopter got into space, it would have to constantly expend fuel to keep up there. To stop spending fuel, it would either fall back down, or have to get going sideways fast enough that it reached orbit speed. Like getting from one corner of a square to another, the shortest route is not go to the top, then go sideways, but to cut through the middle in a diagonal path. Gravity forces it to become a curve instead of a straight diagonal though, but it is still significantly more efficient.