Geez, where to begin?
Glen is right on target if you really want to jump in head first and to keep it simple. The Linn Classik and a pair of monitors (Triangle Titus for $499, Mission 780's, B&W's - lots and lots of nice stuff out there - listen to a couple of them and then pick).
I wouldn't do that, however, if I wanted to get into the hobby as a learning experience - only if I wanted to solve the problem of "I need better sound" so I can get on with my life (and DVD's, of course). If I wanted to learn about audio, I'd keep my money in my pocket - if I were you - UNTIL I had done the following:
1. Learned a bunch about the PROCESS (not products)- for example, how best to ALLOCATE your $1,500 budget to your: receiver, speakers (front, center, surrounds, and sub), source (i.e, DVD, CD), wires (or we call them, cables and interconnects). There have been some nice threads in the last couple of months on this site that will help you sort through this - conceptually, where to get the bang for your buck. If it doesn't start from a conceptual allocation, then any one component along the way can easily blow your budget.
2. Found out what my money could do, say $500 for a receiver? The used market is generally "suspect", but in my opinion, your worries can be greatly allieviated if you stick to the used market on this website, and possibly a couple of others. 99% of the members here at A'gon are honest (100% in my personal experience) and you can get twice the bang for your buck in the used market. You have to know what you're looking for and be patient to find a great deal. Use Google if you're looking for namebrand gear, but stick to this site for the wierd stuff (ha!).
For that receiver, go with the Outlaw Audio 6.1 jobbie for $499, but come to that conclusion on your own after a lot of reading (it's not available for audition because Outlaw Audio is an online only retailer). Or decide on something else. But remember, stick to your budget in terms of the relative amount you spend on each piece of gear.
3. Whenever possible, listen first. The easy thing to do is to narrow the field and then pick a winner and buy it. It's a lot more fun to extend your reasearch and do more comparisons and the end result will be a better match for your musical tastes. Keep an eye on this forum and use the search facility to look at old threads that relate to items you're interested in. Read everything you can about the low budget products for each aspect of your system, and try not to drool too much with the gear that is beyond your price point.
4. Make all of your major decisions in a month or two, and go with what you know at that time. Buy your components as quickly as possible once you start. You don't want to have speakers sitting around for 3 months waiting for the rest of it to come together.
5. Save some money for new music! With your new toys, it will all sound better! There are plenty of websites that will help you to identify audiophile quality recordings that will help any modest system shine.
6. Follow Angela's advice about cables. Keep it simple at first because the sonic improvements that cables add will not be nearly as noticable on a low budget system as they will be as you expand and develop your rig and shrink your retirement savings in the years to come.
Good luck and welcome. Oh, and follow Angela's advice as a general rule of thumb no matter what the subject!