Your idea will work fine, as long as you transfer the old home button to the screen you're replacing. The home button is paired to the logic board for the Touch ID (fingerprint) function.
The part that concerns me about your post is your statement that the 64 GB phone you want to buy has "a broken display and home button". If you mean by that the home button is also broken and not usable, then you won't get Touch ID to work as only Apple can replace a home button. The good news is everything else will work fine if you transfer the entire screen from your old phone, including the home button.
Replacing the screen is one of the more basic repairs for an iPhone and is definitely a good place to start for the novice. There is a good repair guide for your phone available to do exactly what you want.
iPhone 6s Plus Screen Replacement - iFixit Repair Guide
Should the home button on the 64 GB phone be unusable and you don't mind losing Touch ID, then skip the last part from step 24 on about removing the home button and just transfer the entire screen assembly from your existing phone. If you can use the home button, then go ahead and follow the instructions to the end for both phones, moving the home button to the working screen.
Good luck, and if you need help along the way, just ask!
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