How to move only some items from iPhone to new iPhone 6 plus?

I just bought an iPhone 6 plus today and I currently have the 5s. IIm not switching phones until after the new year (cause of work, travel, etc). Plus, I have a lot of content on this phone that I don't want to transfer over to the new one (usually I let whoever working at verizon move everything over - contacts, pictures, etc etc). A lot of the stuff on this phone is not current and unneeded, therefore I only want certain stuff moved over. Can I transfer all of my pictures onto my computer on iPhotos? Or maybe into the cloud? And only transfer some back onto my new phone? I've never used my iCloud so IIm not entirely sure how to use it. Also, I was just going to write down the contacts I need and apps ( a lot of my contacts are old). The only thing IIm worried about is pictures.

On your iPhone 5s, go to settings and iCloud and make sure your signed in. Then turn on all that you want saved. Then click on back up and then back up now so you can keep your contacts, calendar's, etc. Next, sign into iCloud on your 6 plus and restore the iCloud backup. If you want to move over certain apps, you can move them by re-downloading them on the app store, or you can download a program like appandora on your computer and move the apps over. If you do it with the app store, all your apps will be up to date but if you do it with appandora, the apps you moved will be on the same update they were on your 5s. The only problem with appandora is I don't think the new update works on the latest IOS 9.