If I upgrade my iPhone.can I?

I have an iPhone 4s with 16gb and I ran out of space. It's bugging me So MUCH. I can't delete anything else, basically. I went through everything. It's not that I have to many apps, it's what I do on the apps!

I would like to get 32 or 64 gbs but I don't want to loose any of my stuff.
What's the best way to move my stuff onto the (POSSIBLE) new phone?
I'm about to back up my photos onto my computer.
Please ANSWER. 10 points to best person.

ICloud. If you back up through iCloud, once you sign into your new iphone with your iTunes id everything will b just as it was on your previous phone. It's in settings.iCloud storage and back up.

If you have been syncing with iTunes, just plug in your new phone. It will recognize that it's a new iPhone and transfer everything. I did this when got my iPhone 5 and upgraded from the 4.everything transferred perfectly and i had dozens of apps, 1500 songs, 2500 contacts, 1000+pics, etc

You can back up all your info on iCloud. Also, you can ask the person who's helping you with your new phone to transfer all you're apps, photos, contacts, messages, music, etc onto your new phone. It just takes some time depending on how many photos/contacts/music you have.