Still wouldn't use wireless if your first fixing. You say uneconomical but you will be thinking different after a few years worth of lithium batteries.
Yes you are incorrect to have one panel, you will need a much larger area than you think to mount control kit. It's not the zone capacity it's the power supplies and battery capacity that is the deciding factor.
I would be thinking at least PE48 with one PSU200XP possibly more, if using Texe kit from what has been described.
You may want both perimeter and motion detection, pet sensors are not ideal solution if you have a blank slate and are more for retrofiting when a customer gets pets, they can be hit and miss.
360 is more for where you can't cover with standard sensors you don't get the same coverage depending on the ceiling height, ideal for retail environments and maybe on domestic a garage or something but not the norm.
If you go with the company route then don't concern yourself with manufacturer selection, they should use what they are trained on to provide you a good service.