Keep it as bald and laced out as possible … and buy a good shop vac and a fan leaf rake.
You’re going to need them. Set aside 2-4 hrs month to remove/rake the leaves.
Sadly, if the tree is too close to the house, I would have it taken out and the stump ground down. But that is just me. I would be afraid of having to have a new sewer lateral re-dug if the tree is in the front yard, due to tree roots growing through it (if this hasn’t already happened). And also afraid of replacing lifted sidewalks and crumbled driveway … now a very expensive proposition.
Eucies tend to be messy and very time consuming and literally grow wild in the SoCal region.