Hi,
Apple places some items in the DOCK for your thinking you will be using these more than others.
Obviously the Finder is far left.
The Time Machine, Launch Pad and Mission control followed by the App store icon and Dashboard are the next in most people's Docks.
Mine then has Safari, Firefox, Mail, Messages, FaceTime and Contacts.
I then have iPhoto, Preview, iTunes, iBooks, Skitch (Third party app), GarageBand, iWeb, Dreamweaver, Calendar, Pages, Keynote and a few more before System Preferences and Disk Utility.
You can click on these and drag them about into the order you want.
be careful not to take to far above the Dock because if you let go here there is an Animated puff of smoke that denote you have removed the item from the DOCK.
In most cases there are several ways of doing the same thing.
If and App is in the DOCK you can click and Hold to see the menu and Select the Options and Open At Login

The same thing can be done by going to System Preferences > Users and Groups > your Account > Login Items and Pressing the + icon then navigating to the Applications Folder to add an App

Now there are other things that can cause an app to "relaunch" at Start up.
If you do not Shut down/Quit Apps then this alert comes into play

This Alert will restart any App that was Open on Shut down.
The thing that can complicate this is apps where pressing the Red Button does not Quit the App (it only hides the window clicked)
My Messages app with some of my 10 Buddy lists on Display

Having closed/hidden the windows

Hope that helps

9:40 pm Thursday; August 7, 2014
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad