First of all good taste with the game
Now on to your questions: the Elder Scrolls is a series. Oblivion is the fourth installment of that series. Each game in the series is set in the same universe, with the same lore and basic premise, but with a different plot and in a different "age". You don't need any of the other games to play Oblivion because each game in the series is semi-standalone (though the expert will recognise a lot of references to previous The Elder Scrolls (TES) games.)
As for that computer, you should be ok. You won't get maximum settings unless you're using a smaller screen, but it will at least play. However if you could squeeze out a bit more money, try to get the AMD Phenom II x4 925 Quad Core CPU, as it's got a special price at the moment, and will also be better for your overall gaming. If you can also upgrade your GPU to an AMD 6850 1GB, you'll be flying.
Even if you just do a few weekend jobs at the local restaurant or in the newsagents, you could probably get an extra $200 by October, or if you have parents helping you out, you could agree to pay them back if they forwarded you the money. I got a job to pay for my computer, and went from getting a $900 PC to a $2000 PC, so I can tell you that it's well worth the hours of work
Good luck!
-Nih