Hello Rafael from a fellow Tucson ham!
I've been doing SOTA less than a year but I think I'm qualified to say that if you enjoy hiking then yes, this is the Radiosport for you for sure. And just like any sport, part of the fun is the gear. Your HT can get you the 4 QSO's needed to qualify for a summit activation, but it's very likely that you will find HF to be fun enough to justify buying some new gear.
I encourage you to not overthink it. Buy whatever is affordable and get on the air. You won't be disappointed whether it's a 817, KX2/3, MTR, or whatever - all of them will be tremendously fun. If amateur radio is a lifelong hobby you will never stop experimenting with new rigs anyway!
My current SOTA station is usually centered on a KX2. I have not done overnight backpacks with it yet but I do some pretty long hikes (last Friday I took it on a 20-miler to Mica Mountain). I've made close to 2,000 contacts with it and really can't complain about anything.
I've gone on activations with others who have used MTR's very successfully. I owned an 817 way back when they were new (pre-ND version) and loved it. I would say that pretty much any modern radio will give you plenty of operating joy.
Hope to meet up with you at some point, my QTH is Northwest so I usually am involved with the Oro Valley Amateur Radio Club - they are probably the most vibrant and largest of the Tucson area clubs. And when you do head for the hills, be sure to let us know so we can chase you!