I just recently got into comics, and here's where I started. I started with "The Ultimates". Its essentially the Avengers for the Ultimate Marvel Universe. Ultimate Marvel has only been going for a few years, its all new storylines for well known Marvel characters, so theres not too much back log of stories and continuity to worry about.
The Ultimates, is followed by a number of sequels (but not too many!) so you'd be able to read the whole story, and enjoy characters like Capt America, Thor, The Hulk, Giant Man and the Wasp, without spending crazy amounts.
Also, going on at the same time as "The Ultimates" story is Ultimate Xmen and Ultimate Spiderman, which are both really good, but have many more books to get through. Theres also Ultimate Galactus too which is cool. There was also Ultimate Thor, and Ultimate Iron man 1 and 2, which serve as prequels to The Ultimates, so they can be read without any prior comic knowledge whatsoever.
Once you've got your fill of the Ultimate section of comics, its finishes off that particular set of stories with "Ultimatum" - so you have a definitive ending point to aim for.
And after Ultimatum, Marvel relaunched its Ultimate line as "Ultimate Comics". A little confusing, but Ultimate comics are the current line, so you'd be right up to date.
For anymore questions about order etc, check out wikipedia. It's articles tend to explain what comes after what, &tc.