ngl you gotta be careful with that budget for a wedding... that heat is gonna be brutal on the gh6. if i were you, i would suggest prioritizing power and storage over a cage every single time. a cage is nice for mounting stuff but it wont save your shoot if the camera shuts off mid-vows.

• Panasonic DMW-BLK22 2200mAh Lithium-Ion Battery - honestly you need at least three of these. the gh6 is incredibly thirsty and outdoor heat makes the drain even worse. i've seen people miss shots because they were swapping batteries at the wrong time.
• Lexar Professional CFexpress Type B Gold Series 128GB - make sure to get a fast card like this. cheap ones will fail or overheat when you are shooting 4k for long periods. it is a lot more reliable for professional work than just using sd cards.
• SmallRig Full Cage for Panasonic LUMIX GH6 3784 - only get this if you absolutely need to mount a top handle. it helps with protection but doesn't solve your actual power problem. i'd definitely grab the batteries and card first... safety first for a paid gig like that.

I survived a desert shoot without melting my gear.

• SmallRig Sunhood for GH6 3460
• Angelbird 512GB AV PRO CFexpress B Simple, but keeps things cool.

In my experience, I'd actually disagree about skipping the cage. A SmallRig GH6 Full Cage 3784 lets you mount an Anker 737 Power Bank 24000mAh 140W which is huge for weddings. Running external PD power via USB-C keeps the camera way cooler than using internal batteries that just trap heat inside... it's a much better way to handle those long outdoor ceremonies, honestly.