I just used some off-brand, hardware store silicone aerosol and let it sit for 15-20 minutes. Now, it turns very quickly, but the force needed to turn exceeds the force needed to turn it 45 degrees, meaning the absolute minimum i can turn it is 50 degrees or so. When doing a fast solve, I often end up overturing, leading to seconds off my time. I am new to cubing, and open to suggestion.
After applying the silicone spray, you'll want to keep rotating the layers while pressing the cube together slightly.
You should notice two things: firstly, some excess silicone will probably leak out from between the layers. Keep some paper ready to wipe it off, it can eat the stickers pretty bad if your cube has those. Secondly, after a couple of minutes, the stickiness should start to fade, and you get a smoothly moving layer.
Repeat for every layer in every direction.
I think your muscle memory will adjust to the looseness of the cube, so I don't think you have anything to worry about. With more solves, you should find yourself overturning less. For U and D turns, if you aren't already, you can hold the cube so that the same finger (index or ring) on the hand opposite of the finger making the turn rests slightly on the turning face. This way the resting finger tends to stop the turn, aligning it to the cube sides.
Also, if you haven't already, you can try loosening/tightening your cube tensions for a better feel. If all else fails, you can always clean away some lube if that's the feeling you prefer. Since you're starting out, it's more important that you feel comfortable.