How to restore my new iPhone without restoring everything on my old one?

I don't want all of my old text messages/apps/notes/pictures but I do want my contacts and my itunes. Is there a way to just get those back without all of the old messages taking up unnecessary space on my new phone?

Make a backup of your old phone on iTunes. Photos, music, apps, all of it. When you go to set up the new phone DO NOT select 'restore from backup iTunes'. Select 'set up as New iPhone' instead. Then you can pick and select what goes on it but you have all your old stuff stored locally on iTunes in case you want/need it back.
See the this transfer article under the iTunes section. Click and read to the right on the arrow.
Best luck.
http://support.apple.com/.../kb/ht2109