I think that your time signature will be dictated by the text itself - sometimes it's worth looking at the text and working out which words will be stressed and where there'll be gaps if you read it out loud. For example, if you have a stressed syllable every 3 words, then it's more likely to be a triple time signature (try saying the words to 'Twinkle Twinkle' with a stress on every other syllable, then every third one).
As for the key, I'm not sure this is important - as ExpressYourself has said, it's the range which is probably more of a consideration. I think you will need to either choose a voice type (sop, tenor etc.) and write to its range or stick with a reasonably neutral range - if I'm not writing for any particular voice type, I usually stick to a range from around A below middle C, to the D or E in the next octave - this is usually reasonably 'safe'.
When I compose songs, I tend to sit with the words in front of me and play around until I get a bit of tune I like. I then usually work out what key it's likely to be in, and also what time signature it is. My feeling is that if you do it the other way round, in some ways, you're ignoring the natural time/rhythms of the text itself...but...I don't know exactly the task you've been set so I'm not sure any of what I've said helps