I don't think it's ever been a better time to buy computer hardware. If I think back to the heyday, circa 1979, I spent almost $4,000 on a new Apple II plus, which in today's money would've been more than $10,000. Since then, no doubt, I've spent the equivalent of Bill Gate's pocket money on various machines.
A really good strategy today - because we have the Internet community - is to settle on a budget and do your research. A machine that can do all that you've mentioned shouldn't cost more than $1,000-$1,500 - and I'm talking Aussie dollars off the shelf. A forum like this is a great way to ask the 'right' questions and get the 'right' answers...it sure saves time re-inventing the wheel yourself.
First off, each 'application' you want to run will require resources from different parts of your machine. For example, games require a decent, but not expensive, graphics card (GPU) and downloading music and/or videos will need a fast Internet connection - or, at least, access to one. The mistake I've always made is compromise on monitor quality and my eyes have suffered as a result. But, as I said, now is a good time to invest in good hardware, including a big, fast monitor.