Getting Apps from iMac to Iphone via iTunes

I just got a new iPhone SE. I previously had about 30 apps on my old iphone 5 and my IMac through iTunes.

I'm trying to put the "non-standard" apps in iTunes tht I already own onto the new phone, and I'm about to lose my religion doing it....

When I try to sync, by plugging in the new Iphone SE after iTunes is up and running, I get a message that "this iPhne requres a newer version of iTunes" (I'm paraphrasing)

I've Got iTunes 11.4 . When I "Look for upgrades", Itunes tells me it's the latest version.

When I go to the "Apps" section in ITunes, it illustrates the new iPhone; all the "factory" app icon are in color but the ones on my computer/Itunes, beyond the new SE phone "stock" apps, are "grayed out" When I try dragging the older app icons across to the phone, I can't really tell if the iPhone is "getting it", but it doesn't seem to, and the "SYNC" button is grayed out also and useless.

I ABSOLUTELY HATE this new iTunes interface; it acts like something Microsoft would have developed in 1994.

Can anyone help me with thus? I need my "old" apps for my work....

Drew