Personnaly I would go for Gmail...
I've tried many many things as I've had many smartphones over time... so this is what works best for me and what I would recommend any friend!
The only downside I see is that Google knows your contact details... but then, they'd know anyway (if they wanted, they could access your phone numbers, as Android (Samsung S5 runs on that) is from Google !)
It is the safest, easier way to save contacts...
And there are many positive sides:
- you can access your contacts from anywhere in the world, from a computer (can be handy...)
- if you change your phone, just give your gmail address, and boom, all your contacts are on your new phone!
- if you're using Gmail for your emails, you can write emails online (not only from your phone) to your contacts if you added their emails