Beginner Questions about DAW

Greetings everyone,
I've been playing and recording piano improvisations for a while (available here if you're curious) but it's always been amateurish. However, I would like to learn more about DAW and study how to compose structured piece using orchestral instruments (from libraries such as Garritan or EWQL). I first thought about starting with the software Finale 2011 but I play by ear only and I can't read sheet music (I never studied music theory).
Therefore, I'd like to know if anyone could please share advice about what MIDI software may be best to use for a beginner with no music theory knowledge (that's a bad start, I know...).
Also, I am currently using a Yamaha DGX-630 (with MIDI connection, but I still have to test it once I receive the appropriate USB cable), but I am also interested in looking for a better keyboard controller that would be compatible with DAW. If you have any recommendation, I'm all ears.
If I forgot to include any details or information in my description, please don't hesitate to ask and I'll reply as soon as possible.
Thanks in advance for your help.

Really any of them would work well to get started. I would say to check out something simple like Cubase. Also, there is a valuable tool that you really need to have if you are writing piano music. EZ Keys by Toontrack is really powerful as an arranger / chord tool and it also comes with some great documentation to help understand music theory.

Thank you for your reply.
After looking for information on the Internet, I decided to go for the Tascam US122 mk2, and Alesis QX49. As for the DAW, I started working with REAPER (but I might have a quick look into Cubase to see how it looks like).
Hopefully, this should be sufficient to start exploring music composition as a beginner.