Restored my iphone. Unwanted apps keep downloading?

So, i just got a new iphone, i actually wanted it to be new, and not restore it. But i had to restore it because one of my apps from before had alot of data in it that of which i had put alot of effort into making. But anyhow, i only restored it for that one app. Everything else, i don't want. But everytime i finish deleting all the apps, i click sync and EVERYTHING COMES BACK! Like just GO AWAY. But yeah. So is there a way for me to delete the apps without the restoration to re-take place and then syncing it into my computer so i can back it up like that?

When you sync every thing that you had in the past restores back onto your phone, go to the app store and re-download that app you want its self by typing the name in the search bar.