I've been through both sides of the process, having recorded on several occasions in professional level studios, done the tascam multi-tracker thing, and a bit of the "recording on my computer" stuff. I'm a bit of a dinosaur so I use a stand alone multi-tracker still (Korg D3200). I'd have to agree that you couldn't pick a better time to do home recording. There's just so much gear out there, and for the most part, its all cheaper and better than what we had in years past.
A decision that you might want to make is are you doing a "demo" or do you want to make something you can show & sell as a finished product? There are so many avenues for marketing right now, YouTube, Facebook, whatever... chances are if you do a decent job of recording a really great song, its going to catch on somewhere on-line.
A couple of things to add to the great advice already offered. Think about the mix. Do some reading & research, and really pay attention to how you're mixing the music. Don't just create a "wall of sound" with everything recorded in stereo and at the same volume. Learn to place your instruments in both the Left to Right stereo field, and tonally as well, so that a keyboard doesn't cover up a bass line, for example.
Another thing is we didn't use anything too fancy for our multi-tracking stuff, ACCEPT the microphone. I splurged for a Neuman TLM 103 mic and a good mic pre-amp... that really made all the difference in the world when it came time to recording the vocals. You could always cut vocals in a studio, so record everything else cheaply and then spend some bucks on a session for vocals. Saves you buying the gear. We mixed our own CD, but we did take it to a studio to have it professionally mastered before pressing.