Some of the important things you need to keep in mind while buying a new smartphone are-
Check RAM of phone if its less than 1GB it wont be good for Internet access.
Check processor of phone if its having higher generation processor it is good. And will work faster. Prefer quad or penta core or higher version
Check internal memory if its more you will be happy everytime and you may not feel anything like uninstall some apps n keep just a few aps installed only. Preferably go for 8GB or higher memory phones.
If you like selfie then buy phone which is having at least 2 Megapixel front camera.
Check specifications and compare prices on various online sellers before you go to market or order online.
Choose a seller with good reputation by reading reviews about sellers in shopping apps.
Buy a smartphone with proper receipt in order to claim warranty and guarantee in case your phone is damaged.
Check the battery capacity and prefer 2000mAh or higher if you are using Internet on phone.
Preferably choose a smartphone with latest operating systems so that you wont be having any issues with new apps.
Always buy Registered brand phones.