It totally depends on the mood you're going for, and honestly I'd say deciding a time signature, a key, a melody, and a concept are all things that are a part of your decision when composing a piece of your own and there shouldn't really be an answer.
That being said, here's my personal tip: start with trying to find a basic melody, or at least a subject / motif that you will repeat throughout your song. If you can feel the theme of your song usually a rhythm will come from that; rather than deciding and forcing your time signature and mechanically creating a melody from that, try creating your melody and basing your rhythm on that.
My advice personally is to start with 4/4. If you've never composed before or have very little experience with it, I find it to be easier because your measures are automatically divided into equal halves, which are then divided into equal halves on the beat. Triple time (like 3/4) carries the imbalance of the one strong beat to two matched weak beats and if you're more familiar with that style (waltzes are always triple time and you might have experience with that feel) then by all means start there.
If you find a melody you really like and really want to work with but it doesn't seem to work under either, don't be afraid to use compound time (5/4, 7/8) to fit your melody or even move between time signatures during the song. But as a start, I recommend using 4/4 (3/4 but only if you have especially more experience with triple time, for whatever reason that might be) and trying to envision a melody from that, and if that doesn't seem to work, try thinking of a chord progression for both 4/4 and 3/4 and going between them until you find a suitable melody you want.