Congrats on thinking about vegetarianism - it's a big decision and certainly not one to be entered into lightly. I think you'll find that the more research and thought you put into it in the beginning, the easier it will be to follow through on.
I wanted to touch on your questions, as I think they are excellent questions. Probably most people considering vegetarianism or veganism ponder the exact same types of issues. It's good to get a handle on those kinds of issues, both for your own piece of mind and to also have the information for the inevitable debates that occur once you change your eating habits.
The overpopulation of animals is a concern. If all the current meat eaters were to suddenly and irrevocably stop eating meat, there would be a tremendous surge in the population of "food" animals, who would need homes. That would present an interesting and potentially problematic dilemma - how to care for those animals without sacrificing them for food. On the whole, though, I think the vegetarian/vegan movement is more likely to bring about gradual change and reversal, as opposed to a sudden stop, of animal consumption, so hopefully the issue of what to do with those animals will be moot. I imagine the answer will simply be to not breed so many.
If they end up extinct, I'm sure that would be a shame and probably a gross injustice to all "food" animals, but as long as those species weren't being abused and used for human consumption anymore, I don't think I'd consider that a tragedy.
Hunting animals are slightly different. The population of wild "prey" animals are artificially increased by human beings (by the elimination of their natural predators) for the express purpose of there being more animals for human beings to hunt. If left to its own devices nature can control it's own population, through a balance of predators to prey.
Of course, with the way human beings are encroaching on all of the land in existence, we are driving out both predators and prey, which is creating problems with extinction among many species. If human beings want to preserve species, the elimination of hunting as a sport and the protection of environment and habitats should be first priorities.
Dairy cows and battery hens endure just as much abuse and neglect as the animals used for meat; perhaps even more so, because they don't even have the sweet release of death to look forward to after a relatively short period of time.
Human beings are definitely overpopulating the world. That's a given, but a very complex issue. A multitude of things would help improve that problem - better birth control, better education, more meaningful social roles for women, and allowing people to die, rather than keeping the living dead alive. Of course, that particular problem is so multi-factorial - socio-economical, cultural, political, and theological - who knows if it will ever be solved?
You've taken one of the great first steps towards eradicating some of the most common place and insidious instances of animal abuse in the world. I hope you will continue to research vegetarianism and veganism, and consider making the switch. Not only is it better for the animals, but it's a better life style for your health and the environment, as well.
For more information, please consider looking into these sources:
GoVeg.com // Vegetarian 101 (you can get a free vegetarian starter kit here)
and consider reading:
"A Diet for a New America" by John Robbins and "Animal Liberation" by Peter Singer. While both may be a bit dated, they do an excellent job of explaining the impact of eating meat on not just the individual, but the population as a whole.