I've just started playing the guitar. What should I be doing?

I started the same way you did and I turned out fine. I think learning songs actually makes you memorize chords better, and the rifts you are learning will help you will picking patterns and increasing speed. I'd say keep with what you are doing just learn the chords at some point.

i have been playing guitar for 2 and a half years, and i have never had a lesson in my life. and yet, im in 3 bands as the lead guitarist.

my suggestion learn the basic chords ( A B C D E F and G ) if you can learn thoughs chords you can play almost any song.

and do patterns, strum a G chord 8 times, then a C chord 8 times, then an A chord 8 times, and end with a C chord 8 times. once you can switch from chord to chord you should learn a song, by that time your fingers are used to being places on the frets and different stings. some good songs are any acoustic ones, like there is a band called 'secondhand serenade', and he has some easy, but fun acoustic songs.

but no matter what, dont give up. it can be frustrating, but once you can do the basics it will just fly at you. and for just starting out, you dont need to buy anything fancy, see what you like more, acoustic, or electric, then invest into that.

I started the same way man and I think one of the most important things to do is play what you like. Find something that sounds simple enough from a band you like and learn that way. It'll keep you interested and you'll get a feel for what chords work together. I do think it's important to get down the basic open chords too though (A, C, D, E, Am, Dm, Em, and F) I don't know what kind of music you want to play so it's hard to get more specific, but if you're into rock the power chord is your best friend. The best part about power chords is with one shape and 2 or 3 fingers you can play rhythm to mostly every rock song ever written. One other thing I'd suggest is varying your practice time between different chords and fretting single notes. Don't get stuck on practicing like a D/G chord progression for example. You'll get bored and give up; as I said, vary what you're doing. You'll get more comfortable with the fretboard in your hand that way. That's about as much as I can offer without knowing your style of play; just remember, play what you love and what sounds good to you, not what someone tells you you have to. Cheers.

A tuner is really helpful. Also A tutor, you can get one really cheap and they are usually really good people with mad skill. Buy a beginners CD. They Teach you how to work on your skill, plus if your finger pick'n you need to get callouses on your finger tips first. Lost of work, good luck