How to effectively search for apps on/without using Google Play?
Try combined search words to narrow down the result list. If you e.g. look for an alarm reminder, "alarm reminder" gives you 1.000+ results -- while "alarm-reminder" (note the "minus" replacing the space) shrinks it to 48, relating to both terms (and not just either one of them).

Sometimes also the rules from Google's main search engine apply here (I could not yet figure out when they do and when they don't). So "alarm +reminder" should list only apps whose name/description contains both terms -- while "alarm -reminder" should list only those containing "alarm" but not "reminder". As said, this works sometimes, while the first rule mentioned seems to work always.

I just tested it, and surprisingly even some more advanced keywords work: "clock +intitle:alarm" really lists only apps having "alarm" in their name (and "clock" in their name or description; though this I did not verify completely). I suspect the playstore search is just a "customized Google search" -- so you might play with other "tipps and tricks" from its "big brother".