I'm a complete newbie when it comes to guitars. Lately I've been interested in a new hobby that I could do at home so I thought about learning to play. I'd like to know, how long does it take most people to start playing decently? By decent I mean playing a full song without too much difficulty (it can be an easy song though)

Totaly depends on how motivated You are if you dont have a guitar teacher chances are you will give up and never be able to play a full song. Go to a local music store their will probibly be a wall of music teachers offering lessons.
Glad to hear you've taken up guitar, one of the best moves I have ever made. I finally got an interactive hobby, not some stupid collection or something. And I agree with twist, there are many factors that can determine how long it takes to "get good at guitar." I could play Radio by Alkaline Trio (bad song, but easy and teaches some decent techniques -alt. picking, palm muting, etc.) in about two weeks. But I would still mess up frequently, couldn't play it perfectly.
Yeah Dimebag is not the "Greatest Guitarist" of all time... Hendrix maybe... I must go get food to eat with my mouth

$250 for an amp? wow. is it worth it to invest that much in the amp?

Depends on what you do. My motto is, always go for the jugular. The hardest stuff you can possibly find, and learn it. Take it slow, and eventually youll play it, though crappily. Keep learning hard songs, and youll be better in a few years than most will ever be in 20 years of experience. Most people learn really really slow because they are not guided properly, not motivated enough, or only stay on the easy stuff and dont want a challenge
It depends on what you define to play decent. If you want to play Green Day, it will take you no time. If you want to play shred, it will take you some years of hard work.
It all depends on the person.

Yeah...i've been playing for about 2 months now and i can pretty much play songs like Smells like Teen Spirit and Killing in the Name........but i practice about 5 hours a day(yeh i know i have a lot of free time). But time flies when you're havin fun