kjamesuvic: Save your money until you have $200 and then buy yourself a bottle of Octomore.

Sorry, bad joke... but in all seriousness, there is some good and some questionable advice here. My two cents, but you shouldn't feel the need to "work your way up" to quality Single Malt Scotch by drinking cheap blended whisky. Also, you most certainly don't want to "kill your taste buds". One of the most pleasurable aspects of drinking fine whisky is honing your sense of taste and smell.
I was going to reference
this post I made in a similar topic, but your budget and chances of finding like-minded individuals your age willing to pony up some cash will make it challenging (read: impossible).
As some people here suggested, start off with one solid Single Malt within your budget. Most of the time, that means Glenlivet 12yr or Glenfiddich 12yr. They're cheap, readily available, and have an accessible flavor profile (mild mannered, light, a little fruity, a little grassy). They're also a little boring. Huntsman made two excellent suggestions (Cragganmore or HP12) that are in alignment with your budget and offer a little more character than the previously mentioned whiskies while still maintaining an accessible profile. Oban does get recommended pretty frequently, but I tend to steer people toward Cragganmore since Oban does have a detectable bitter/metallic finish. In the end, Diageo's still going to get your money. The Glenrothes, Old Pultney, or Dalwhinnie will also get the job done.
When you do acquire your first bottle, find a quiet time to enjoy it where you won't have many distractions (particularly strong aromas in the air). Call over a couple friends who you trust won't just try to shoot it...
Sorry, getting side tracked here, but once, I was at a business function and the guy hosting asked me to pick a Scotch off the restaurant's menu with little or no concern about the price. I saw that HP18 was fairly priced and he ordered a round for everyone at the table. To my horror, half the people present shot their whisky and then made sour faces. I wanted to cry.
Anyway, when serving your whisky, try to use something tapered like changy suggested. A wine glass would be better than a tumbler to help focus the aromas. A cheap brandy snifter would be even better (probably not going to be able to afford Glencairn glasses on your budget at this time... spend your money on whisky instead). Only pour 1-2oz at a time. Give it a few minutes to breathe. Smell your whisky (but not too deeply). Try to pay attention to what you're smelling. Take a tiny sip neat. The alcohol will burn your mouth and palate at first. Take another tiny sip. This time, you should be able to taste a little more of what's going on. As you're slowly enjoying your whisky, add a few drops of room temperature filtered or bottled water at a time and see how the smell and taste evolves. Have some discussion with your companions about what they're experiencing (sherry, peat, grass, malted barley, salt, brine, sea aromas, berries, nuts, etc. etc. etc.). Have fond thoughts of your grandfather and when he used to enjoy a little Scotch.
Or not. I'd imagine a lot of 21yr old kids would think this is all rather douchey and pretentious. If that's the case, spend your $50 on 90 cans of Simpler Times at Trader Joe's instead and let the good times roll.
The topic of when one should drink whisky is also heavily debated. There are many who enjoy a nice whisky after a heavy meal as a digestif. There are others who try to put as much time between their last meal and their whisky as possible since their palate will be at its freshest. But you should already know the pitfalls associated with drinking on an empty stomach. You also can't argue with having a dram of Scotch with a juicy steak. I think the answer is that there is no bad time to have some Scotch.
After that first bottle is gone and your interest is still there, try something a little different. Perhaps something a little bolder and a little peatier. Until you're a little more familiar with the different styles of Scotch, I'd recommend holding off on any of the whiskies from Islay (like Ardbeg or Laphroaig). Now that is something you may need to work your way up to.