I want to improve more than playing for “fun”. However I enjoy chess when I am improving.
If improving is more important than fun, then I can't offer any advice. I agree with Preggo, enjoyment is important. For me, improvement happens to come from enjoyment (or fun). The only way I can do that is by not not playing all the time. If I play too much, it's not fun because I am missing out on more important things in life. Chess is a social game for me and the only reason I play is to have fun with the people I play against. I've stopped playing online for a couple months, but still play with friends on game night. Plus it's summer, who wants to play chess in summer?
Hi CleverOak
As someone who has already improved compared to what he was before I advise you to:
1) Avoid thinking that you're talented, that idea held me back for a while and when I stopped it I focused more on studying and training and that helped me improving.
2) Get some good chess books on different aspects of the game (I can recommend you some if you would like) and when you read a variation try as much as you can to do it in your mind rather than on the chess board.
3) Have patience and don't be hasty, chess improvement takes years of studying, training and playing. Remember what Mark Dvoretsky said: "Don't expect immediate results, but have firm confidence in eventual success."
4) There is a lot of useful training tools here, especially Tactics Trainer, try to solve as many puzzles each day as you can even if you fail mostly at the beginning, it helps much in calculation and in sharpening your tactical vision.
5) Try to play as much chess as you can without getting exhausted or bored or enslaved by the game, all types of chess help in improving certain factors of your game. I don't know how we define "true chess" and I wonder how "true" rapid and blitz chess are compared to the classical one but even bullet helped me in improving two factors: First is remembering many opening traps in which I used to fall into, Second is improving my ability to think and play fast, you know I used to be troubled by the shortage of time but after playing tons of bullet games I play rapid or blitz feeling that I have enough time to play.