Before I start its important to know why you have rooted your device.
REMEMBER DONT ROOT UNTIL YOU HAVE SOME NEED OTHER WISE IT MAY HARM YOUR PHONE. ROOTING GIVES EXTRA PERMISIONS SO YOUR PHONE DATA BECOMES UNSAFE.
Now whatever your reasons may be dont modify or delete any important file without knowledge as this can make your phone bricked.
First of all what you have to do is backup your original or stock rom by using titanium backup or rom manager. Its important to backup your stock rom as if you bricked your phone you can restore your phone by reflashing the stock rom by using odin flash or clockworkmod recovery.
Now find a guide to install cwm recovery in your device which help you in restore or install customs roms.
Dont restart your phone before doing this or your phone may hang on logo or gets brick.
Now if you have rooted what are the apps you should install.
Clean master: If you have install this app this is the first app to access superuser request to uninstall inbuilt apps or to move apps to sd card.
Freedom: If you are fed up with in app purchase then freedom has the solution. Freedom acess you free in app purchase with its freedom xxx card. You can buy anything. Check on how to use freedom.apk
Weaver: If you gets an wifi but cant use it as this is password protected then weaver can help it cracks password using root access and help you use password.
Gl to sd: This app can move all your apps to memory card and help you free up some space.
Directory bind: This app is award winning app it can move your data files to external sd card without disturbing your app. When the data is moved only the size of app is stays on phone memory and saves lots of data.
Link to sd: This app requires sd card partition with root access to work. But the app is great for low memory phones.Chainfire: The app is a great work of masterpiece. The app works well with low end phones as the work of app is to run any type of game without lags. This app changes graphics settings and use nvidia graphics plugin to run high end hd games.
SO THESE ARE THE APPS YOU CAN INSTALL WHEN YOU HAVE ROOTED YOUR PHONE.