I think a good way to progress is to follow this general path.
1. Pick a character.
2. On the character forums, read about the character in particular and learn how to use them.
3. Begin practicing all basic moves. You want to be able to perform any move on command at any point in time.
4. Begin to practice one or two tech skills as you sharpen your basic skills. I started with L-cancelling and short hopping which are probably the most important tech skills in the game.
5. Watch tourney vids with pros using your character. This will give you ideas for combos and teach you how to use your character.
6. Practice every day for at least 30 minutes. You want to get that muscle memory going. CPU matches arent the best, but you should be able to use them to get technically better.
7. Start going to tournaments and/or find people you can practice with. Money match people if you have to. I think this is how KDJ got good. He just kept money matching people and kept losing, but eventually it gave him the experience he needed to succeed.
7. Repeat the process with other characters so that you don't get bored.
Good Luck!