One thing that might be tripping you up is that modern digital gear (almost) always completely separates the radio transceiver from any motor drivers. That FlySky you linked is a perfectly decent kit, more than capable of doing what you're after, but you still need an ESC to go between it and any motors you have. Based on your description, you'd need three (cheap and common) brushed ESCs (something cheap and simple like this random example would be fine). You can map channels to inputs arbitrarily, so you can set the lift motor to a switch (off/100%) or to the throttle channel, and you can do a simple mix for proportional differential steering with the other stick.