How to transfer one iphone to another & delete icloud etc off old phone?

I have a new iphone and a new sim card, I think I know how to back up my old phone on iTunes, but to sell the phone on I need to delete icloud etc but when I put the new sim in my new phone the old one won't work, so as soon as I back up the old one, do I delete everything after and then sync the new phone? Also the computer I'm doing the transfer through is a bit slow, once I've done the sync, can I delete iTunes off the computer or will it need to remain?

The option on the phone for "erase all content and settings", it will ask for your password, then its wiped clean after that and you are good to go!

Just back it up in itunes first.

Sync old phone for a complete backup copy in iTunes on pc. Settings > iCloud > Turn Find my iPhone off > at the bottom, Delete Account (from the phone). Then Settings > General > Reset. Erases the entire phone back to factory. Plug in new phone to iTunes, either set up as a new phone or 'Restore from iTunes Backup'. Go into iCloud set back up like you had on the old one. No, never delete iTunes from your pc. Always keep a recent sync backup copy of the phone there in case loss/theft and your iCloud gets gunked up or something. Best luck.

All of your info/apps etc. Are stored in icloud and on your account, so if you logged into a new phone, it should come up and then you can just erase data off your old phone.