I think I can find the key signature of this song I'm trying to notate(What's the word?) but how do I know if it is quarter notes or eigth notes because I could say either and just change the tempo?
You're talking about the time signature. The easiest thing you can do when in doubt, is to count it out.
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There are various convnetions for choosing whether you count the time out in crotchets or quavers etc. but it tend to just be what is easiest and most natural. You wouldn't put it in 200bpm quavers over a much more moderate 100bpm crotchets in most circumstances.

When you count it in your head what notes do you count?

the same is true of key signatures - you could technically write your song in A# major and put it in about 10 sharps (you have to use double sharps in some cases *shudder*) or you could put it in a much more user friendly Bb major with 2 flats. They're exactly enharmonic but there are technical reasons why you may pick one over the other, however writing music is a form of communicating it. so to quote einstein "everything should be made as simple as possible, but no simpler" in other words communicate your music in the simplest possible way while still keeping it as your music with the same ideas and emotions.
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