This question covers a lot of ground, but I'll make some assumptions about your situation:
When it comes to sensor tech, companies like Optex and Takex offer high-end equipment - so I'd be curious to know what you found after looking at those offerings. Chances are, if those offerings had a difficult time, less expensive commodity sensors would struggle more. As you've found, selecting the correct outdoor sensor is not a simple thing - there are many environmental variables like heat, humidity, precipitation, heat gradients, and line of sight that determine overall effectiveness.
Brian K is correct when he writes "A typical installation of a couple of cameras, mounts, wiring, etc. is going to be a few thousand dollars minimum. However, many of the higher-end outdoor motions aren't much cheaper". I cannot vouch for VideoIQs analytic accuracy, but he is right regarding cost. A high-end system is costly - and it still can be fraught with false alarms if improperly designed.
As far as remote notifications (email/SMS), those are generally a function of the alarm panel, and not sensors. Most modern alarm panels have a dialer module that can be configured to notify you, even if the system is 'unmonitored' by a central station. However, you might check Alpha Arsenal that sells simple PIRs that can be paired with GSM cards for 'panelless' remote notification.
You might also find our Xandem report useful. That intrusion technology is built around a 'tomographic' field that is immune to line of sight problems, and is tuned to alarm on human movement. The technology claims very low 'false alarm' rates.
Like Brian K offers, there are many factors that weight into the 'right' choice, and following up with more details about your situation will help get you the best answer.