I’m a fan of insulating first because I find it more pleasant to have the house stay at the same temp longer rather than cycling between too hot and then too cold when the AC is running every couple of minutes.
We did a combination of R-38 batt insulation in the attic and blow in (i.e. drill & fill) for the exterior walls and it’s helped tremendously. Also, we added radiant heat barriers in the garage where there’s no HVAC. We had pros install all of this since it is fairly labor intensive to crawl around in the attic. They knocked it out in 2 days.
Another thing we did was get solar panels. Depending on your state’s current net metering policy, this could more than offset your entire usage. For us it made sense since we were also getting an EV in addition to having ever-increasingly hot summers.
If I had to replace the AC unit, I might look into a heat pump/mini-split like you mentioned since you don’t have to cool/heat the entire house if you don’t need to, but ours is still fairly new.