I've really been meaning to rewrite and change the OP as it's severely outdated (and a lot of the links don't work), I'll get around to that...some time.
I'd recommend you buy some small MIDI keyboard like
Novation Launchkey,
Korg MicroKey,
or IK iRIG Keys
Then, if you don't already have one, get an audio interface. The main reason you want to use one instead of the onboard sound on your computer is for low latency ASIO drivers (and onboard sound cards are pretty shitty, sound quality wise), which reduces latency using MIDI keyboards and other MIDI related things.
Steinberg UR22 or
Presonus Audiobox.
Lastly, you'll want the software you'll be doing production in which are called Digital Audio Workstations (DAWs). There's a large number of them, at various price ranges. There's not really any "better" or "worse" here, they all have their pros and cons. They all have demos, so download them and give them a try and see which one you feel most comfortable with and get that.
In no particular order (with prices next to them)
Ableton Live 9 -- Standard $500, currently on sale for the holidays for $359
here. Very popular with modern music producers.
Cubase 8 -- Pro $549. One of the original programs for computer music production, first version dates back to the late 80s. Also popular with modern music producers.
Presonus Studio One -- Professional $200, currently on sale for $139
here. Relatively new, but well regarded.
Bitwig Studio -- $449, currently on sale for the holidays for $255
here, add to cart to see discount. Very new (came out earlier this year), had a bit of a rocky launch, but recent patches and current discounts seems to have improved general opinion about it.
FL Studio -- Producer Edition $200. A lot of people's "entry" point into computer music production, has a silly stigma that it's for "kids" and beginners, but it's fully featured and more than capable of producing professional songs.
Sonar X3 -- $79, available for $59 on Steam and a few other places. Not commonly used by electronic/hip hop producers, but is fully featured and seemingly stable.
Renoise -- $89. Has a very different interface from everything else on here, a bit esoteric (but is actually my personal favorite). Has some shortcomings when it comes to recording audio.
Reaper -- $60. Has quite a large cult following. Cheap, stable, fully featured.
Reason -- $399, on sale for $340
here, add to cart to see discount. A self-contained production environment. Every other program here is capable of using 3rd party plugins (VST/AU), this one cannot. Instead, it uses proprietary instruments and effects made by the developers and community. It's decently popular with electronic music producers.
Native Instruments Maschine Mikro -- $350. Quite different from everything else on here. It's a very specialized software/hardware combination that has some shortcomings, specifically if you were into recording live instruments (like drums, guitars), but it's very fun and fast.
There's more, but that's off the top of my head. Note that a lot of those programs have varying price points and different editions. I chose the cheapest edition for each program that didn't have any crippling limitations, like lack of plugin support.
I personally recommend some of the more expensive programs like Reason, Bitwig, Studio One, and Cubase. Not because they're better, but because they come with a lot of instruments, effects, and sounds, so you don't need to go out and scour for free plugins and samples (at least initially). Reason in particular has pretty much everything you need built in. Ableton is an exception here, as Ableton Live Standard is mostly sampled instruments and effects, Ableton Live Suite is much more expensive but includes more synthesizers. However, as I said before, try out the demos for all of them and pick the one you think you'd be most comfortable with. They're mostly really expensive, so you shouldn't just spend the large amounts of money they're asking for without doing a decent amount of personal research and making sure you get what you really want.
Another thing to note is that your speakers are likely not "really" suited towards production and most producers use near field monitors like
KRK Rokit 5s. That doesn't mean you can't use your speakers, but you need to be diligent about checking out how your songs sound on different sound systems (ipod headphones, car stereos, etc.) which you should do anyway, really. If you live in an apartment or have room mates, you may want to consider a pair of headphones like
Audio-Technica ATH-M50 for late night work.
Edit: Oh, J10 already got you covered.