'Progression' and 'nothing hardcore' generally don't go in the same sentence unless the phrase 'is totally different than goofing around and doing' is between them. The former implies significant time investment in the form of research, practice, and optimization. The latter is what most of the playerbase does (there's nothing wrong with that. They're just very, very different approaches).
Based on what you're asking for, you seem to be in search of a light RP FC that also spends time on relatively casual content. There are a lot of those. Step into Ul'dah and you'll trip over a dozen.
With all due respect, I'm inclined to believe that no, you did not look hard enough.
Tl;dr - Join a roleplaying FC and look in PF if you want to do midcore content, or find/form a static if you're feeling more ambitious once you get to 60.
Based on what you're asking for, you seem to be in search of a light RP FC that also spends time on relatively casual content. There are a lot of those. Step into Ul'dah and you'll trip over a dozen.
With all due respect, I'm inclined to believe that no, you did not look hard enough.
Tl;dr - Join a roleplaying FC and look in PF if you want to do midcore content, or find/form a static if you're feeling more ambitious once you get to 60.