If you have an acoustic guitar I STRONGLY suggest learning on that. Your fingers will get stronger a lot faster and you'll get valuable practice learning how to get the cleanest fretting.
This.
Just because professional musicians and accomplished guitar players can tune by ear doesn't mean it's a good idea to have a tuner. The few times I've tried to tune by ear my guitar ends up out of tune. I don't see any harm in dropping $20 for a digital tuner if it means that your guitar can be 100% in tune any time you want it to be.
Tuning your guitar by ear is not hard. It's difficult if your guitar is has bad intonation, which is a staple of cheap guitars. However, that can be adjusted simply with a screwdriver. However, I still suggest that you get a tuner. In fact, in order to adjust the intonation you need a tuner anyways, so get one.
The best thing you can do for yourself as a musician is to learn theory first, and the instrument itself later. If you play piano, grab a music theory book and do a page a day on your piano. Learn your key signatures, intervals, chord types, rhythms, how to write your own music (on a grand staff), etc. The worst thing you can do is just go along playing the guitar with a bunch of tabs.
