There are 3 common lamp socket sizes used on residential lamps.

Candelabra Sockets E12 size, hold small size bulbs with a base diameter that is slightly under 1/2".  This size is used on chandeliers, wall sconces, small lamps & night lights.

Edison Sockets E26 size hold normal size bulbs with a base diameter of approximately 1". They are the most common size used in table lamps. 

Mogul Sockets E39 size hold large bulbs with a base diameter of approximately 1½". This size is often used on floor lamps.

There are 4 main socket switch types

Turn Knob is a switch style that's available in both on-off and 3-way dimming options. To operate switch, knob is rotated to position. There are a wide variety of socket types that use this style switch. 

Push Thru is an easy to use on-off option. Simply push stem to on or off position. This is often the most economical choice when looking for a basic socket.

Pull Chain is a great option for lamps with a lamp shade, as it is easier to pull the chain than to reach up under shade to access switch. The lamp many need steading when pulling chain.

Keyless Sockets have no built in switch, as a result a cord switch or wall switch is required. This style is ideal for wall mount lighting and hanging lamps.

Standard sockets typically offer multiple switch types, while specialty sockets may feature a single, optimized design. When choosing a socket consider that the socket switch affects how you interact with your lamp.