Peach Tree - help

Hi,

I have a peach tree in the backyard. Last year it produced a lot of peaches and unfortunately the weight of the tree broke one of the two main branches. One side of the tree is still alive but not producing any peaches and the other side is pretty well dead.

Should we just cut it down and remove it? Keep the stump? Looks like we have suckers growing from the base of the tree - I was thinking of cutting it all down and letting the suckers grow?

Also, it is right on the side of the house, probably affecting the foundation of the house?

(p.s. this in my rental place, I am just an awesome tenant trying to help out the landlord but have zero knowledge on peach trees)