NewThingsAreFun:
Hello my fellow Arduino mates (is there any specific term? Sorry, a newbie here!)
idea is to connect a smartphone/computer (through HTML?)
You probably meant HTTP, not HTML. One is a communication protocol, the other is a markup language.
NewThingsAreFun:
I have to use a wifi shield or can I also use an ethernet shield with a router? Which will be easier?
To communicate over Ethernet wireless or wired, you'll need either a wifi shield or an Ethernet shield.
Home security systems are a common Arduino project...