Could you give me any advice once how I should proceed with 3D logo placed on the ground in regular footage, that will reflect the ground texture and cast shadow?
I’ve already tried extruding with ray tracing rendering method, but it does not allow me to cast a shadow on the ground (blending options seems not supported in ray traced 3D) - however I can overcome this with making some blurred opaque solid that will work as a shadow, and maybe use layer mapping (I have never used it before) to create reflections.
But I am also wondering about these 2, maybe better solutions:
Element 3D works like a charm for such things and a whole lot more, and it is integrated right into AE, using AE lights and camera. And renders lightning fast. For a simple setup like you're describing it is virtually real-time.
There is also the (free) option of using Cinema4D Lite, which is integrated with AE somewhat similarly, albeit more clunkily. There is a significant difference in rendering speed.
If you use Blender, getting the camera angles to match between AE and Blender cameras is... well, difficult. There are some export import scripts for transfering data between the two programs, but I wouldn't call that a simple approach. Of course, if you do all animation in Blender and only non-camera related effects in AE, that could work.
Personally I use Element for most things 3D inside AE, it's both fast and easy. That would be my recommendation.