I agree with Aimless. You may feel fine with being uncomfortable now, in the city, indoors, but when you're actually in the uncomfortable situation, for real, you won't be. (I know I'm not.) The problem is, you won't have the skills, knowledge, or gear to do anything about it - and now you're in precisely the kind of situation where hypothermia and dehydration can be life-threatening.

Check with local colleges, to see if any offer some type of outdoors course (many do.) If you find one, get the training and go on a few of the beginner trips they offer. You'll quickly catch on, and you'll pick up a lot of tips. This is not a difficult pastime to become competent in, and the rewards are bountiful. However, running out into the woods, totally inexperienced, will see you return home vowing never to set foot there again.

As far as gear, you don't really need a lot of space to store it: it should all store inside the pack itself, so you're not talking about something any larger than an airline carry-on bag. If you really don't have room for that, there is another option: rent gear for your trips from one of those colleges I mentioned earlier, or from a backpacking shop like REI. That's also a good idea until you get some experience; you can learn what does and doesn't work, then pick out your own gear based on that experience.

But for now, scale back your aspirations.