Generally, the pump is installed at the basement's low point. That way, the water can be channeled there using gravity to move the water to it.
If you put it at, say, a high point or in the center of the garage, water may pool in places because it can't run up hill or across the floor until there's a sufficient amount of water present.
You should have drain pipe leading to the pump because you don't want it to 'collect', even naturally. W/O seeing the landscaping around the basement or the basement itself, it's hard to say what you should really do. HOWEVER, if you know where the water comes in, and it's only at one point, then you may be able to get away with just installing a pit and a pump. Do the install right. Otherwise, we'll be hearing from you on how to 'fix' this.
As an aside, you should survey the gutters and downspouts and landscaping around the ENTIRE house. (Water travels in mysterious ways.) In the next (preferably) heavy rain, go outside to see if gutters are leaking or overflowing. Check for downspouts that dump water less than 3' from the foundation. Check that you have POSITIVE sloping AWAY from the entire foundation for at least a distance of 3'. Fix leaking or overflowing gutters, extend downspouts if necessary, and create POSITIVE sloping away from the foundation to see if your problem goes away. For 90 percent of the cases I've seen, these are what contributes to water in the basement. Rarely, is it an underground stream and rarely is the landscape unable to be re-graded.