Gonna be very hard to answer your question, as you have not told us anything about the 15"/220 watt amp. I suspect you are making some common beginner mistakes about the amp, and PA's in general.
First, noobs often look on the back of an amp or PA head and see something like "115 volts, 220 watts" and assume it is a "220 watt amp." Not by any meaningful measure, it isn't. That's the wattage it PULLS from the duplex wall outlet, NOT it's power output. That's sorta like saying that, since your car holds 20 gallons of gas, and a gallon of gas has approx. 11,000 watts of energy in it, which converts to abut 15 horsepower, you have a 300 horsepower car. It's not that easy. That is a measure of POWER INPUT to the amp, NOT POWER OUTPUT. If it really had 220 watts output, it should have little trouble keeping up with drums and most guitar amps. Something is not adding up.
And where did you get the idea something is putting out 550 watts?? Perhaps you meant 220 watts?
That PA you posted may have stuff you already have, like mics and cables, and things you don't really need, like speaker stands. Stands are nice to have, but you can put the speakers on top of shelves or crates or such, and do as well, at least in your rehearsal space. You don't tell us what your drummer is like (does he hit hard, or does he have a real sense of dynamics?) what kind of amps your guitarist(s) or bassist have (20-watt solid state practice amps, or 100-watt twin 12 tube amps?) or the size and reverberation in your rehearsal space. If no one is going "monster," you might do well with a little 100-watt PA system (Custom makes one,) which sells for $200, new. Still, there does seem to be a lot of value in that system, so if you can use all that stuff, you could do a lot worse.
Keep in mind, that system has TWO 150-watt self-powered (that means the amplifier for them is inside the speaker case) speakers, or 300 watts. That is most likely going to handily out-perform that thing your singer got. You might want to try using your singer's PA as a mock sub-woofer, placed in between the two 12" speakers- it might help, and with the others, you won't need to crank it as much, so you might get in below where it distorts.
I am suspicious of those Behringer powered speakers, when I read something like "
One of the coolest things about active loudspeakers is the lack of backbreaking racks of amps, crossovers, and EQs that are often required to make passive speaker systems sound almost as good. But that comes with a trade-off?:;that extra weight is transferred to the loudspeaker, making it difficult for a single user to heave all that mass onto the top of a speaker stand." What a CROCK! There is just so much bullshit there, I don't know where to begin- but suffice to say that if a manufacturer is saying that kind of horse pucky in it's ad copy, you gotta wonder what the REAL story is.
Confirm that Guitar Center is going to extend the 30-day return refund to your PA (GET IT IN WRITING, AND READ THE SMALL PRINT), I'd try out that Alesis system- it may well work well for you. If not, return it and go up a step or two.
(I tried to keep that simple and to the point, and not bore you with too much tech stuff, or confuse you with too many alternatives.)