I would begin by doing the math. Mini excavator rental cost to do the jobs vs cost to buy the enticing shiny orange backhoe.There will of course be residual value meaning what you might sell it for down the road to consider. Often when your jobs are done you end up tripping over it and perhaps making payments on it. Its easy to justify the purchase when the the promise of fulfilling work is in front of you. There is a great line in the fabulous book Blood Meridian by Cormac McCarthy "There is no joy in the tavern as upon the road thereto" . Skip the backhoe buy the book.
I would guess the rental of a mini ex would win EVERY time over the backhoe purchase,
for one project.
Having bought a backhoe 20 years ago for my tractor, there is certainly no way I would have rented a mini ex every time I wanted to do a small job/project around the homestead. Would not have been cost effective. So small things would not have gotten done. Or would have with GREAT PHYSICAL EFFORT on my part.
Couple years ago, I bought an old mini ex, and it is head and shoulders better than my tractor backhoe, all around, and both have about the same reach and depth capability. I still can't give up the tractor backhoe though.
On the tractor I can get where I want to go faster and with less damage to the ground surface (not that this matters much to me). BUT the mini ex shines for what it can do digging, and placing the spoils wherever you want, in a 360 degree circle.
If it is for the long term, buy the backhoe for the tractor. If for limited projects with no interest in doing little things along the way, rent the excavator.
My take on it anyway...