Planning a 3-day south coast tour in Iceland – any tips?

I'm heading to Iceland in early July for a short 3-day break and want to do the south coast tour from Reykjavik. I'm thinking of joining a small group tour that includes Jökulsárlón lagoon and ice caving.

Has anyone done a similar 3-day south coast trip? How was the pacing – was there enough time at the main stops or did it feel rushed? Also any advice on what to wear and bring for the ice cave part in July?

Thanks!