I think my corp (Tuskers) is what you’re looking for. We’re a relaxed (no minimum activity levels, no CTAs, fly what you want, when you want etc.) mature solo/small gang PvP corp. We use out of game comms (Slack) to communicate, which makes joining fights even easier - a simple ping means when you do log on, there’s something going on.
Historically, we were a low sec pirate corp, but most of us have found more fun living in a Class 2 Wormhole with a static NS & C5 for PvP & logistics/PvE respectively. We think this wormhole offers the best mixture of logistics & PvP - the direct NS gives us plenty of opportunity for fights (at the moment we are getting about 50-80 kills per day) and the C5 gives us decent logistics.
We run a mixture of organised & impromptu gangs. 95% of our gangs are impromptu, basically a few guys heading out together or asking for backup.