If the EG112 is the one I'm thinking of, then it's a decent starting guitar to have. If you're a new player (which I'm assuming) then the guitar you're using doesn't really matter though - what matters is that it's in good condition, properly tuned and intonated, and all the electrics work. As long as that's the case, you'll be fine, and you can worry about getting a better guitar when you know enough about the instrument to know what it is that you want.
I've never put any thought into a guitar tuner - I always got mine by going into music shops and asking what they had. They're all pretty much the same though, so just get the cheapest one that does what you want it to.
You should work on tuning your guitar by ear, though. There are plenty of tuners you can find online for free which will play the note for you, then you just tune your string until it sounds right. If you're able to do this, you'll be a better guitarist.