Prefer a camera that has better/bigger sensor. The larger the sensor, the image quality will be generally better. In many situations, you will not see the benefit of it but as you get into low light situations or fast moving objects, a bigger sensor can take you few steps ahead of others.
As you can see, a dSLR has 13 times bigger sensor compared to a compact camera. The bigger the sensor, the camera will be able to take better photos for you. Also, newer camera models have better sensor technologies. They are more sensitive to light and are able to take relatively better photos compared to older sensors. In good light, this does not make difference but in low light, it does.
#1- This number shows how wide the lens opens. You can call it aperture number. It starts with ‘1:’ or sometimes with f or F. The smaller the numbers after ‘1:’ or f/F, the better the lens will perform in most situations. 1:2.8 (often mentioned as f/2.8) takes in more light than 1:4. A camera with 1:1.8 will normally cost twice as much as a camera with a lens that has 1:2.8 but will let roughly 4 times more light during same amount of time.
#2- This is the focal length, or range of focal length, of the lens. The bigger the numbers, the better it will be. Normally bigger numbers imply bigger sensor inside the camera. Please remember the weight on the word Normally in the sentence. Some camera manufacturers put these numbers as 35mm equivalent. Be suspicious if your compact camera has starting number bigger than 20!
Focal length is the distance between lens and camera sensor.
Now how to make sense between these two numbers. In example able, for a focal length 4.8mm, if it is f/2.8, it means that at this setting, the lens will open 1.74mm! If you take a photo without zooming and say the camera uses f/8 aperture, in simple language, this means that camera will open the lens 0.6mm!!! Do you know how tiny that number is? Can you imagine how much light can go through that tiny whole particularly when you are shooting in low light?
I often use a 50mm Super Takumar f/1.4 lens on Pentax APS-C (Digital or Mirrorless cameras). Btw, this is a 40 year old lens but try to hold it in a hand and you will see how much we are losing in terms of mass production in this plastic age! So when I shoot with 50mm and 1.4 aperture value, the lens opens staggering 36mm!!! Compare that to the 1.74mm the lens opens maximum for the compact camera that I was refering above.