We are a Small acapella vocal quartet looking for an economical but well put together sound system comprising wireless mics (preferably head mics) amplifiers and speakers. The Bose L1 looks very good but I think it'll be out of our price range. Any guidance is welcomed.
The Bose L1 is a good smaller-venue setup for giving the sound some lift- easy to use and natural. Whether it would work for you I guess depends on how much gain you need from it. It does progressively less well in high-gain and high-volume situations with larger numbers of inputs.
If the L1 is too pricey for you, that basically leaves a whole compendium of powered mixers and "speakers on sticks." A decent lower-cost option that still isn't a complete compromise (like Behringer or some of the lowest-end gear) is something like the Yamaha EMX 212S and a pair of Yamaha SM12V's on sticks:
Keep in mind you're still going to spend around $1300, and that's before mics. If you think that's too expensive still, I would suggest you look at getting something that's used and better quality rather than compromising quality even more.
If you're looking at wireless and head mics for 4 singers, that's likely to add at least $2200 to the bottom line for anything that's not complete garbage. I always suggest that bands stay away from wireless unless absolutely necessary, or unless they're willing to commit enough resources to it to get decent-quality gear that will also be reliable.
Much to my surprise, the B52 Matrix 2000 is a pretty decent system. However you don't need the sub, so I'd go with something like the FBT Maxx series speakers. (I've mixed shows on the Bose -for the money, I am not a fan.)