Just top up the gearbox oil first, its cheap & dead easy, it should take 2 litres, I got 1.5+ litres into my last one so must have been only half a litre in there. The whine went pretty much but after another 3000mls the box went BANG!
The gearbox oil filler allen bung is on the end of the gearbox behind the front passenger side wheel. You squirt the new oil in there until it overflows out of the hole then you know that its at the correct level.
If that doesn't sort it, there's not much cash or time wasted and you can start looking elsewhere.
All three of my Golfs came with very low gearbox oil, its one of the first things to check when you buy one.