After having all 3, the best one I've bought and my family loves most if the Lenovo Smart Display with Google Assistant integrated to it. The built in screen is just adds sooo much more features than the Echo or home. But I still use my home mini since it can be connected to my smart display, and use my Echo in the bathroom.
After trying all 3, I recommend get the Lenovo Smart Display instead. Especially with the not so far apart price, and a built in screen that just adds so much more feature, and the camera shutter. I mean I can go on, but it would be a long post. To keep it short, if you're on the budget, get the Lenovo Smart Display.