I'm a fellow addict...
Love, love, love the challenge of the game. First question - are you a decent athlete? Hand-eye coordination is key. For the full swing - see a pro. They love to teach the full swing. My first lesson was when I was 21, with a physicist who worked for NASA who was also a golf pro. He taught me grip, stance and posture, how to swing, and then taught me a few simple drills for the long game (driver and irons) that really showed me how to self correct and improve on my own. I'd be happy to share those if you're interested.
My recommendation for learning the game -
Learn to put the ball in the hole first - find a way to make 10 3'-0 putts in a row. Then back out and try to make 10 4'-0 putts in a row.
Then, find a 'flatter faced club' like a 7 or 8 iron, and practice the 'bump and run' chip. Back a pace or so off the green, and learn how to get the ball into that 3 or 4 foot circle so your putter can take over. Read the chips like a putt.
After you can bump and run it pretty good, then take a lofted club, like a pitching wedge or sand wedge and learn how to 'pop' the ball up and land it on a spot, and let it run toward the hole.
Basically - if you can get your short game sharp, the long game just gets you around the green so the short game can take over. The more time you spend on the short game, the better you will be.
The long game will come in HUGE chunks of improvement. You learn to hit the ball without slicing, you learn to take a proper divot with the irons etc... Your scores will drop dramatically with the long game coming around, and then the short game makes you a player.