Chamaerops Humilis palms sucker freely. No, I'm not using a silly word here, that's the term applied to a plant like this that send offshoots from the base. So they want to grow in a bushy shape. If you are constantly struggling to keep the sucker growth under control, under the mistaken impression that this is a non-suckering, single-trunk palm, you are gonna have a bad time.
I've had this one (pictured) for many years now and have only just given it its first trim this morning. And while it's not a job you will need to do often, it's a nasty job. Those fronds are sharp!
So, to do it safely, start from the top and be prepared to do two cuts on each branch. The first cut will remove the fronds, with those nasty razor-sharp thorns, and then the second cut will be to trim the stub down for neatness. Leaving stubs on palm trees isn't bad for the tree, it's just ugly. I will actually go back later and trim the stubs down as far as I can. You can't "skin" a med palm the way that you can do to a Mexican Fan, so don't try it.
The best trick for easy cleanup is to throw the cut fronds on a tarp. Then instead of trying to carry a handful of needles (ouch!), you just fold the tarp up around the edges, and take it to the trash. There will be a bit of work as the thorns dig into the tarp to get them to release, but it's better the tarp than your skin!
Work, work, work. I'll probably have to do this again in another five years.
By the way, yes, you can get med palms (Chamaerops Humilis) at your local Home Depot or Walmart. They grow slowly so buy one in a five or fifteen-gallon pot. They don't mind the heat, but I really can't recommend planting one in Phoenix right now (for your sake, it's over 100 degrees during the day). Plant it in the the spring, from February on.