MRT2

I will take a whack at this.

What to look for new or used.
Aluminum or Cro Moly steel frame. Carbon frame would be nice, but probably not in the cards unless you are looking to spend some money.
Carbon fork is a plus, but not a dealbreaker if the fork is aluminum or steel.
8 speed or higher. Because all 8 speed and higher come with a freehub, which is a better design than the older freewheel you find on most 7 speeds.
1 x , 2 x , or 3x are all good. It really is a matter of personal choice whether you want a bike with a front derailleur and 2 or 3 front chainrings. Advantages of 1 x is simplicity of shifting. Disadvantages. Unless you are going with 1 x 11, you might find yourself with either big jumps between gears. On the other hand, some people just hate shifting between chainrings, so in that case, a 1 x is better.
Drivetrain components. Shimano Altus components or higher. (Acera, Alivio, Deore for mountain groups, Claris, Sora, Tiagra, 105 or higher for road groups. I used older 9 speed Tiagra on my main bike and I like it a lot. My wife has an older version of Claris shifters and I don't like them as much, but they do work reasonably well. If I were buying a hybrid, I would look for Acera or better.
No Shimano Tourney or similar entry level stuff from other brands like Microshift.
Hydraulic discs are nice but not essential unless you are spending more than $1,000 t. Otherwise, mechanical discs or rim brakes are fine.
And speaking of brakes, you will often find bikes spec'd with Tektro brakes instead of Shimano. That is fine, actually.

What generally isn't great on any lower priced new bike priced below $1,000, and even sometimes on bikes priced above $1,000.
Wheels and tires. When the tires wear out you will replace them with something better. And depending on your weight and how you ride, you might want to replace the wheels.
Brake pads - Switching from the stock brake pads to kool stop salmon pads made a huge difference in my braking performance.