which out of these two cables/ports is best for my miniDV camcorder?

Hi all,

I have a Sony MiniDV handycam model DCR HC 18. I understand that using
Firewire connection to transfer video to PC (and subsequently for
burning DVD out of it) provides a better quality as compared to USB.
Now I am not sure which is the firewire port in my PC/Laptop. My
Handycam has an output marked 'DV out' and with a symbol 'i' near it
(second output from left out of four outputs present) that I
understand is the output where firewire cable is to be connected
(there is another output near it (first from left) with a USB sign on
it). Now, my problem is like this:

I have two cables, which both fit in the 'DV out' port of the
handycam. Out of these two, one cable is having identical connector at
the other end, and my laptop and my Desktop both have a port which
matches this. The second cable is having a slightly bigger connector
at the other end (of the size of a USB connector but thinned out
slightly from one side, sorry I don't know what it is called). My
Desktop has a receptacle for this as well, whereas my Laptop doesn't.

I am not sure which cable out of these two gives a better quality
video. Please suggest.
Also, what is the 'LANC' output (fourth from left and last output
provided on the handycam)?

Thankyou