What is the best way to transfer data from Android with a broken LCD to a new phone?

[MrJozroz]

My Galaxy S5's LCD broke and I've ordered a Huawei Honor 8 as a replacement. Whats' the best way to transfer data from the Samsung, including messages, contacts, photos, apps. Basically everything. What's the best option in terms of cost (preferably none), reliability and trustworthiness?

Back when I worked at an electronics superstore, they had a program that automatically transferred all of that (practically creating a carbon copy) between phones, but I cannot recall what it was called, and even if I did I'm reluctant to pay a huge sum of money for something I will use very few times in my life.

 

[Sam_Gs7]

All the Phone carriers Can do that. When you go to Activate
the new Huawei they can Transfer all the Data: There're other
ways to Do that, but their Technic is effective: Try it on!

 

[MrJozroz]

Neither phones are attached to specific carriers, I simply purchased the phone alone without a carrier contract, so if I take it to a store's tech support they'll charge me extra. I could do that, but I'd rather fix it myself if possible.