Moving a telephone jack and wiring it
Key question is: How many phone lines do you have?

If you have one phone line then you only need 2 wires - one pair. This will normally be red &amp; green on the jack and a colored pair of wires from the wall.

If you have two phone lines then you need 4 wires - two pairs. This will normally be red &amp; green on the jack for one line, black &amp; yellow on the jack for the second line and two colored pairs from the wall.

With normal phone service (POTS), you can have the wires in a pair reversed without a problem. However, you need to make sure the pairs themselves are not mixed up.

You can reuse the existing wall jack. But I highly recommend getting a new jack like Leviton 40249-W Standard Telephone Wall Jack, 6P4C, Screw Terminals, White. With a new jack that uses screw terminals you will not need any special tools to connect the wires - just strip the ends and screw in place. A wall jack will require either an electrical box or a box eliminator (a metal or plastic "frame" that is the same size height/width as a box but no depth - just cut a rectangle and stick it in) or use a Surface Mount Jack instead.

So all you really need to figure out is 1 line or 2 and which pairs of wires from the wall go to line 1 and (if you have 2 lines) line 2.

I am assuming your VOIP is some sort of magic box (e.g., Magicjack, Vonage, etc.) that lets you connect regular phones to a VOIP line. If that is not the case then none of this wiring makes sense. With one line (no matter how many phones) you only use 2 wires (red &amp; green) of the standard 4-wire configuration. You just need to figure out (hard for me to tell from the picture) which pair of wires connects to the red &amp; green on the inner part of the existing jack. That pair should be connected to red &amp; green of a new jack, screw terminals recommended. (FYI, the existing jack needs a punch tool to do it right, which phone &amp; network installers have but the average DIY does not).

Don't worry about the mess in the basement. If/when you fix it up, if you use the same cable to this location then you won't have to change anything on this end, just in the basement.