Have you got a community choir or something similar nearby? If you find one with the right person / people leading, it should be an opportunity to sing and learn about singing that is free or inexpensive and also gives you the chance to meet others who enjoy singing too. I go to a weekly small choir where I work and, over the past couple of years I have been attending, have noticed a definite improvement in my ability and confidence.
There are a lot of vocal exercises you can do on your own. Also, I think most people are pretty good about giving free advice on what they know. You just got to be brave and ask (in the right setting). If you are around some great vocalists, you can ask them what they do to "wood-shed" or basic tips to control pitch, volume, lung capacity and other vocal colourings/techniques.
However, the best bang-for-your-buck is probably like you suggested. Get a cheap video camera (or USB one) and record yourself singing some well known songs. Compare those to either the original or other covers on you-tube. If you're brave, send them off to the other to critique (or even upload to YouTube). I am almost willing to give you a money-back guarentee you will:
a) Feel really crappy about yourself. (Ever wonder why they say the camera adds 10 lbs?)
b) Quickly improve or refuse to tape yourself ever again.
It's amazing what very accurate reproductions of yourself can do. It shows you your warts and all. Much better than the traditional mirror, since your can keep playing it back and re-assess yourself.
I haven't done the video part, but definitely done the audio part regularly when I was actively leading a worship team. Learned a lot about myself. I found out about issues that I had never known about.