It's more than likely the vga connector which you get will have all 15 pins. Its shape has to physically match the connector on your computer. However you will solder wires to only 6 of the pins. If it does not display properly then you may need to solder the additional 7 wires (as shown in the second pinout table).
Are you planning to use a crt tv? It will make a fuzzy computer display. I have used a crt type with my laptop's S-video output. I cannot even read most of the text. However it is great when watching videos. The tv is brighter and has a larger screen.