And it could be the mouse is acting "hinky" because it's not fully compatible with the MAC. The cursor is hanging up a bit, not moving smoothly.
No, a mouse not being fully Macintosh compatible really isn't a thing. Usually when I've seen what you are describing the cause is either that your mouse is too far away from your computer (signal loss, usually made worse by something existing in between the two), or there is some sort of interference from something like a florescent desk lamp, cordless telephone, or some other appliance.
You will have to pay attention to this, because it might present a problem with *any* wireless mouse you buy.
By and large, if any mouse is going to be problematic, it's going to be a Bluetooth mouse. I tend not to recommend them. I usually recommend Logitech mice, specifically the ones with an "RF" wireless interface rather than Bluetooth. RF requires that you take up a USB port with a beaver-tooth dongle, but the vastly increased reliability is worth it.
One's choice of mouse is very personal, but I tend to love this model:
Logitech M310 wireless, optical, ergonomic mouse
$20 from:
https://www.amazon.com/Logitech-Wireless-Mouse-M310-Flame/dp/B004ZEZB88/ref=sr_1_7
Oh, just another data point, but I have never had any problems with Logitech's optional mouse software. You really don't even need it if you don't want to change any of the standard features of the mouse, but I personally love to tweet my mice to suit me. There IS a problem in that Logitech makes many different versions of their free mouse software available for download, and you have to get the exact right version for it to work perfectly with the mouse you get. Once you get the right version, the software is very powerful!