Since you're on Mac, I vote for Garageband to start with. You can look at other DAW's later on. Logic is a great option on Mac, I use Reaper but I'm on Windows.
I pretty much agree with all the other stuff said here too, although FWIW I've done all my recording, mixing and mastering on headphones (I do check with the living room speakers though, which are not great either), and feel like the quality is good enough for me.
One thing I would focus on more than others is that you get a good workflow down that helps you get stuff recorded. Having a low barrier to firing up a session and recording something valuable, because you get more done. Sometimes you might not feel like doing it if the barrier is higher (you need to move stuff around or plug/unplug things, for example).
Like others said, don't stress about having fancy plugins, complicated tools or mixing techniques. Panning and levels does a lot, add a little EQ and you're cooking, a bit of compression (although it can be tricky as a beginner) and reverb, and you can get a really good result. Especially if you're not recording drums - but that is a whole another can of worms anyway.