There are two primary considerations with regards to the motor: where it is mounted, and how much power it has.
With regards to mounting location, keep in mind that in general you want to equally distribute the weight of a bicycle across the entire bike. Equally distributing the weight makes it easier to balance and improves traction, which makes it easier to handle the bike. Another consideration with the mounting location of the motor is tire maintenance. Wheels with motors mounted in the hub are harder to work on. See the summary below for a comparison of eBike motor drive types:
Mounted to your pedals
The motor’s torque is applied to the chain or belt, allowing it to work with your bike's gears
The ride typically feels more natural
Best balanced
Better at climbing hills
Tend to be more efficient (can go further on a single charge)
Tend to be more expensive
Mounted in the rear wheel
The motor's torque is applied to the wheel, independently of your bike's gears (this isn't as efficient)
Might feel like the motor is pushing you
Good ratio of price to performance
Puts more weight on the back tire (easier for front tire to lift off ground, or not get as much traction). This problem can be compounded if you are carrying gear on the back of your bike.
Mounted in the front wheel
The motor's torque is applied to the wheel, independently of your bike's gears (this isn't as efficient)
Might feel like the motor is pulling you
Less traction than other options because there is less weight on the front wheel
Typically used in less expensive, easy to install, do-it-yourself conversion kits
eBike motors are typically marketed by wattage. It is important to know that the wattage number seen when looking at eBike specifications should be taken with a very large grain of salt. There is no standard or even consistent way to provide a numeric 'watts rating' for a motor system. You can see the exact same motor listed as 250 Watts, 500 Watts, and 1000 Watts by different manufacturers. At the technical level, a bike motor can have several different wattage ratings, such as "nominal" wattage, "peak" wattage, "continuous power" wattage, etc. Making published numbers even more meaningless, you will find that "brand name" manufacturers like Bosch and Yamaha—who need to sell into a regulated market—will publish smaller, more conservative wattage numbers, because they want their bikes to be "legal" in more places; while other manufacturers will list the higher numbers because they may not care about those markets as much as they want to advertise their motors with seemingly more powerful numbers (even when they aren't). And then you also have un-reputable manufacturers who publish the absolute highest wattage level the motor will take before exploding.
A quality 500W motor is more than enough for casual riders and commuters. A 250W motor is a fairly low power motor, but it can be enough for light use. Heavier weights (both for bikes and people) will require more wattage to go the same distance. Motors with higher power ratings will require heavier and more expensive batteries to go the same distance. Like anything, motors can vary in quality, including efficiency, noise level, durability, and reliability.
Motors will often also indicate how much Torque they can produce in Newton Meters (Nm). Torque is a measurement of force (usually in rotation). In the eBike world, torque (Nm) gets you up hills at low speeds. Power (Watts) controls (limits) how fast you can go up that hill.
Think of it this way: Torque is what gets you started. Power is what gives you speed. Take cars and semi trucks as an example: Semi trucks have motors with very high torque (and lots of gears for torque multiplication) so they can pull an 80,000 pound load from a standstill at a traffic light. Typical cars cannot do that. At the same time, a semi truck is horsepower (think of horsepower as Watts) limited so that it crawls up the hill that your car can zoom up.
This means a bike with higher torque is easier to get going from a stop, or start on an incline. The more newton-meters of torque your motor can produce, the less hard your legs have to work to turn the pedals on your bike.
Recommendation: If you can afford it, look for an eBike with a mid-drive motor. While you will want to know the wattage rating (and torque) on your eBike's motor, remember that the same motor can be listed with different wattage ratings by different manufacturers. You will need to do some research to make sure what kind of measurements are being used, and take into consideration the brand's reputation. Try to find reputable (independent) reviews of the bike (See my Resources page).