I would not get in any hurry upgrading any clubs. Get to learn the courses and play mechanics with the starters for a while.
You will feel the urge to do the opposite, however, start upgrading clubs starting at the green and working backwards.
You hit the putter more than any club in the bag so get a good putter first.
To have a chance to get close to the hole, start replacing the wedges and you will learn how to put the ball closer and closer to the hole. You can ditch the 3H early to get a 3rd wedge. The 56 deg wedge will fit between your PW and the 60 deg and 64 deg wedges.
You can then start with better irons, driver and 3W.
Somewhere along the way start playing a lower-cost ball with some spin. Don't worry about the distance at first. You can get some spin with 10-64 credit sleeves and you will learn how to hold greens with these balls and the better irons and wedges.
The main thing is to practice. Some of it is very repetitive, but that is how you learn how to make shots and see how different courses and holes play.
Others noted to get into a "good" CC. Included in my definition of a "good" CC is not only one that is active and has a fair amount of CC tournaments, but one that has a fair mix of tiers - including the higher tiers. These are the players that can really help with your game. Many of them are very willing to help the lower tiers - don't be afraid to ask.
Have fun and don't get too caught up in trying to win tournaments all the time. That gets to be a grind and is not much fun while you are needing to learn!