I've been using the Sony AX700 with an MK1 recently to film more casual stuff and it's a really nice camera for size and price. It has the zoom rocker, which is nice if you are filming others, or you could try filming in 4K which might allow for zoom in post production.
You could try looking at the Sony AX100 on ebay, which seems to be a bit cheaper. I'm not entirely sure what the difference is between the AX100 and 700, but I think it's still a good quality camera.
You could also look at a used HVX or HPX on eBay, it seems like they are less than $1K now.
Keep in mind, you will probably need editing software and a laptop to get videos from camera -> computer -> instagram.