This is a tough question to answer because everyone has a different need.
Here are some general rules for a casual rider.
Brand
You will want to stick with the more common bike brands. This will help steer you towards a better quality bike. Some brands include: Kona, Trek, Norco, and Giant. If you’re looking for a kids bike, you can also look into the quality brands Cleary, Spawn, and Frog. A better quality bike brand tends to have better quality parts. Better quality parts means the bike can ride properly, and more importantly, safely.
An unsuspecting entry level brand that works well is Northrock at Costco (frame is manufactured by Giant). If you do decide to go with the Northrock (or another bike from a department store), I’d recommend you have a knowledgable mechanic tune the bike before riding.

Brakes
disc brakes are pretty ubiquitous these days but there are differences between the types of disc brakes. Hydraulic disc brakes have fluid inside the line (similar to a car). These brakes need to be serviced regularly to ensure the brakes work properly. The cost of servicing these brakes is not typically covered in a standard tune up.

On the other hand, mechanical disc brakes use a standard mountain bike brake cable to actuate the brake pad so there is less maintenance and can be adjusted during a typical tune up.

Linear brakes (also known more commonly as a v-brake) are a great, simple, and powerful (if set up properly) option.

Wheels
Wheels are typically one of the areas a bike manufacturer will try to save money and cheap out. It will be hard to tell the quality without looking at brand and model. Your goal is to make sure the wheel is as straight as possible before you buy it, both new and used. Simply lift up one end of the bike and inspect the distance between the rim and brake pad or frame. You shouldn’t see much wobble in the rim.

Shifting
Shimano components tend to rule the market but you’ll see many bikes with the brand SRAM also. Reliable and accurate shifting is a factor of many things but you can get an idea of the shifting quality by the rear derailleur on the bike. For the casual rider, you will want to look for a “Shimano Tourney”, “Shimano Acera”, or “Shimano Altus” level rear derailleur. If you are looking at a used bike, there will be a wider range of quality levels you may notice (Shimano LX, STX, XT, Alivio, Zee, SLX). Buying a bike with a non branded rear derailleur almost always ends up costing you more in the long run.


Test Ride
Take the bike for a test ride. There is nothing worse than buying a bike that looks good but doesn’t fit or feel right. Comfort is important but things like grips and seats can be changed for your body type.
Bonus Tip
If you’re buying a used bike, always budget for a tune up to ensure the bike is safe to ride and the parts work as they should.
