Apple's Logic pro if your on mac, and Abelton if your on windows are good choices. Those are the two I've used most. I used FL studio when I started out, but I prefer the first two.
Cubase I've tried, cakewalk, etc;
I think the first two I mentioned are very good choices fro someone just starting out.
You want something that has allot straight out the box for you to learn from.
With Logic for example, it has a ton of plugins already built in. Synths, effects, everything.
If you learn those well, (and many of them are great synths) You learn the basics that will carry over into everything you're doing.
So pick a DAW that has allot of stuff already in there that you can be getting on with.
The worst thing is getting something and it being bare bones, meaning you have to go and buy a ton of expensive software to make anything decent.
As others have mentioned, get a decent pair of headphones. Don't buy some crap from Monster though and think price equates good (Beats).
There are allot of ridiculously priced headphones that are basically just fashion accessories. You don't want that.
Rather than Monster or Skull candy, Try AKG for example.
Go for respectable audio companies rather than corporate giants trying rake in the cash from dumb consumers who haven't done their research.
There are speakers too, monitors, which in general are better. You get a much wider sound and better clarity.
However, your room presumably isn't acoustically treated, so there's not much point to go for monitors yet.
Once you get into it more, these in my opinion should be your next purchase.
