Either way works. I once had to do it the iCloud way because my phone borked (hard) while I was at a conference - and I sync with my iMac, so no, I didn't have the machine with me at the conference. It was "uncomfortable" at first, because (3 or 4 years ago) it took a while for my contacts to just go ahead and sync with the new phone, and I was more than a little anxious that everything wouldn't migrate. It did.
I think iCloud is much more robust today than it was then, and I keep calendars and contacts there so they sync among all of my devices.
I think it's easiest and quickest to simply plug the phone into your computer at home and sync it that way. Less chance for errors to crop up, and so on... And of course you can quickly wipe the phone and then restore it using iTunes, so that's a plus too.