Neither of these features are important.
Remote -- is a convenience feature. Prevents you from walking to other side of the court to press a button. It is kind of a necessity if you are training someone and need a pause to show or explain something.
Oscillator is only a neccesity if you have kids, specifically 2 kids, and they both want to play at the same time.
Depth. My machine does not have random depth variation. It might be convenient if you want to practice net shots -- with varying trajectories of the ball coming at you. Sometimes, I have to practice running up to drop shots. This is another circumstance where it might help. I have to run to the back of the court, so that I could run up again.
I've had the machine for 5+ years, and when I use (as opposed to my kids), I only use straight up shots -- to hone a particular shot.
Machine cannot be a substitute for playing, and trying to force it to play like a partner is going to be futile.
For me, far more important factors: (1) how does it fit in the trunk and (2) how does it recharge.