Computer: If the computer you asked this question on belongs to you, is less than about 2 years old and is not an i3, Pentium or Celeron, it should be fine. Older Athlon X2 or Intel Core 2 Duo/Quad machines are passable, but edging toward obsolete for modern DAWs, especially when you'll be using a lot of VST plugins as with EDM. A Celeron, Pentium or other budget PC marketed to casual users for browsing and e-mail won't have the clocks for the real-time parallel processing a DAW needs.
If you really need a new computer, you should be able to get a laptop from Best Buy, or the guts for a new one from NewEgg or TigerDirect, that will be more than enough for DAW work. Look for a CPU in about the $200 range (that'll be newer i5s, older i7s or AMD FX-8xxx), at least 8GB RAM, at least 1TB HDD (and consider investing in an external HDD and/or cloud storage; audio takes a lot of storage), and if you can still get Windows 7 pre-loaded, IMO that's better than Windows 8/8.1 for audio work (a lot of audio drivers and VSTs aren't stable on Win8 yet). You can get a computer with the specs I just gave for well under a grand, especially if you're swapping out the guts of an existing mid-tower (if all you're doing is replacing CPU/RAM/Mobo and adding some HDDs, the tab can be less than $500 for a screaming rig).
The computer above will be all you'll need for quite some time running a DAW, and won't be half-bad for gaming and other processor-intensive uses either. And this is if your current computer will just not cut it; if your computer was marketed as a gaming rig anywhere in the last 4-5 years it should be fine for DAW work. You don't need a MBP, nor a $3000 gaming rig.
DAW: Reaper is free to use indefinitely (the trial is ostensibly 60 days, but they don't lock down or neuter the software after that), and when your conscience (or the nag screen) gets the best of you it's $60 for a personal non-commercial license. It's a very good DAW too, with a very lightweight framework leaving more "sandbox" for the plugins, and a hardcore and fast-growing following in small project studios where it's compared favorably to the popular expensive monoliths like Pro Tools, Logic, Cubase, SONAR and Ableton.
Keyboard: What you'll want for DAW use is a "MIDI Controller" keyboard, as opposed to a "Digital Piano", "Stage Piano/Keyboard" or "MIDI Workstation", all of which have features you don't need or don't do things you'll want. MIDI controllers are available anywhere between $100 and $1000, with really good ones in the $250-$500 range if you don't mind a "synth-action" keybed and less than 88 keys. Check out the Novation Impulse, Akai MPK and M-Audio Axiom lines, which all come in frame sizes ranging from 25 to 61 keys, and also include pad triggers and assignable fader, knob and button controls for mouseless control of basic DAW and plugin functions. If you're a piano player and really want that same feel, there are a few controllers with 88-key "hammer-weighted" keybeds like the M-Audio Oxygen 88, but those cost more especially if you want the pads and other assignable controls. You might look in the used market for a Roland Fantom or Yamaha Motif workstation; these retail for between $1000-$4000, but sell used for half that or less, and would be the last keyboard you'd ever need.
VSTs: Reaper comes with the basics for free: compression/limiting, gating/ducking, EQ, reverb, even pitch correction and a synthesizer and sampler. If you want more, there are a bunch of quality freeware VSTs available online.
Sample Libraries/Virtual Instruments: Usually a notable subclass of VSTs, sample libraries controlled by a MIDI-compliant software engine basically give you a computer-based version of what you'd have in a $1600 workstation (and sometimes much more). Kontakt is dominant, nearly ubiquitous; the full version is a bit spendy at $400, but there's a free version, Kontakt Player, that's bundled with third-party patch libraries (most still pay-to-play unfortunately), and also available separately with a few freeware libraries like NI's own Factory Selection. The big downside of staying free is that you can only use sample libraries not specifically marked for Kontakt Player for 15 minutes at a time; for unlimited use of most of the freeware NKI libraries available for Kontakt, you need the full version.
All is not lost, however. To get your feet wet, I recommend staying old-school by using SoundFonts. These are an older library standard developed by Creative Labs for their SoundBlaster cards, and picked up by Yamaha, Roland and others as an easy way to load and transfer samples between equipment. There is a free VST available from Cubase, SFZ, which plays any of the massive number of SoundFont files available for free online. Sinfonia is a common go-to SoundFont for orchestral-type instruments, and Chorium is also a popular one still used today.
There are also freeware synth VSTs. Synth1 and Crystal are two tools practically every home recordist has in their arsenal; Synth1 is an excellent virtual analog synth, has a lot of excellent sounds in it reminiscent of the trance heyday of the late '90s, early '00s. Crystal is a sampler, with free patch libraries available from a number of sources.
Existing Music: YouTube is free.
Other things you may need that you didn't list:
Microphone: Vocals aren't a requisite for EDM, but they're common. You'll also probably want some sort of recording setup for sampling. An AT2020 is available for around $50 and it's an excellent place to start for a studio mic. You can also get the Sterling SP30 and SP50 as a set for $60, though this is starting to venture into a really hit-or-miss pricepoint. The MXL990 and 991 are also a common entry-level studio condenser set, of much better quality, for about $120.
Audio Interface: If you want to use pro-audio microphones, you'll need an audio interface to get the signals into the computer; the average consumer-grade sound card mic and line inputs don't support these types of sources. There are plenty of great products in the $150-$200 range. I have the Focusrite Scarlett 2i4 and like its simplicity (USB-powered, no control software) and flexibility (2 inputs for XLR or 1/4" TS/TRS, 4 outputs either TRS or RCA, DIN I/O for older MIDI devices, and very flexible "direct monitoring" capabilities). Its microphone gain leaves a bit to be desired for low-output dynamic microphones, and high-Z inputs peak easily, but it's fine for condenser mics and line-in sources. Other good choices include the Scarlett 2i2, Presonus AudioBox, Steinberg UR22, and Mackie Onyx Blackjack.
Good listening equipment: When you're building your mixes, you'll need equipment that faithfully reproduces what you're listening to, so when you apply an EQ or set the relative level of any two channels, the resulting sound you hear is not colored by a natural response curve of "hi-fi" systems (even expensive consumer brands like Beats Audio or JBL) that emphasize bass and high mids, or cheap computer speakers with totally unpredictable response ranges. Studio reference headphones and near-field monitors are designed for flat, extended response curves, so you hear everything in your mix, and the amount of each frequency is accurate. This generally isn't as pleasing to the ear as a hi-fi system's response, but that's for a good reason; if it sounds good in studio monitors, it'll sound good through almost anything else.
Reference-quality gear is spendy; monitoring headphones typically run from $100 to $300 (I got my ATH-M45s on sale for half price at $50) and "near-field monitors" with flat response curves and good bass response, designed to be placed in an equilateral triangle with your head about 1m on a side, start at about $250 per speaker. For now, you can use a hi-fi shelf system to listen at your workstation, and you should also take the mix around to any other audio system you have access to, from your iPod and cheapie ear buds to your home theater, your car stereo, any pro audio system you or a friend might have for DJing, etc etc. If it sounds good through all of these, then it's good to go.