If I put from iphone 6,sim card to new unlocked iph6S will it work right away?

My att plan is until sept this year? Thats not important for now. Ill deal with that later.
General question is how to have a iphone6S right away/as soon as possible. How to settled new iphone6S with my sim card from iphone6 and transfer all data from one to inother one ( iTune perhaps)

It will not work at all you would have to buy another slims card for that new phone

Yes. But both phones have to work on the same network. The new phone is either unlocked or is an att phone.

I don't think the iTunes stuff is saved to your sim. You will need to back it up today your iCloud or iTunes account.