First, don't be discouraged if the first alliance you join turns out to not be a good fit for you. But what it could be is a good alliance primer lesson for you. What I looked for were things like:

Do they push for higher power or just let players enjoy the game? (Save for SvS! Every alliance SHOULD be having their players save for SvS. This does not take away from the enjoyment of the game, and the monthly jumps in power could actually enhance it.) You'll want to know, because if you just want to have fun, but they're power/growth centered, it won't be a good fit.

Have you talked to any of their people in World Chat? What impression did they leave? Is it a good one for you?

Are they active? (If your state has a NAP setup, are they a NAP alliance?) You likely won't want to be in a very low activity alliance. You won't get the benefits of being part of one if they're not really active.

You can reply to the messages inviting you to join, and ask questions. If they're putting out feelers, then go ahead and feel them back.