which speakers should I buy?

So you want wireless and like horns?

Lot of PA stuff that will work, if you're into volume, and a certain amount of quality.. But Horns for outside do work well.. Just look, to keep anything covered, in severe weather.. Some of the horn loaded bass systems, will rock the WHOLE block. BIG boom boom.  They can be simi-outdoored. Mine have lasted in shops, 30-40 years..Still going in some.. Big suspended horns 10-15 feet up.. A couple looked like upright pianos, and the weight, was close..:-)

Big Class d 12k Behringers. 3500 watts @ 4 ohms.. 550.00 ea.
But there has to wire somewhere, right? Big bang for the buck..

Just an Idea....

either speaker wire or power cords. This may not be the first place to shop for active outdoor speakers. 

I guess power cord is ok. I’d like an active speaker. Quality trumps volume for me. What about these battery driven speakers, vifa B & O etc? Are those horrible ?

contact hifibuys in Atlanta. They do custom installs with systems that specifically designed for outdoor audio. 

   I assume by "patio" you mean open-air outside space.  If not, forget what follows.  I'm in CA so mine is set up year-round.
  IMO, outdoor listening is quite unlike indoor listening -- where reflections, room configurations, carpets, drapes -- are mostly irrelevant to out-door listening.  I've experimented with several approaches over the years. I hauled floor standers and subwoofers outside for parties, tried multiple speaker arrays for a surround experience, and finally hooked up a pair of ancient 60 Hz Henry Kloss  "Cambridge" outdoors to an Alexa and digital amp for the pool and spa in my latest home.  
  You can't expect detail like you do indoors. Nature's concert venue provides a broad mid-range with adequate treble (not shrill at all)  and surprisingly acceptable bass.  Be mindful that your neighbors will appreciate not having you select their music for them.  
  So, I suggest you start with an inexpensive set of outdoor speakers (and a spool of inexpensive speaker wire), then experiment with multiple heights and placements.  I'd use an existing lower end amp or receiver and a voice controlled music source for several listening positions.  If you want more, then you already know why and how.