One thing to consider if you are going to use the internet on your phone is how much information you can get on your screen.
Computer screens and mobile phones screens are divided up into small squares called pixels. Obviously the more pixels on your screen the more you can see.
For example my large computer screen at home is 1920x1080 pixels.
Now I am afraid the phone you have been bought is at the rather low end and the screen is only 320x240 pixels so it is not going to be able to display a lot of data when on the internet.
Just to compare, the Samsung Galaxy Fame is 480x320 pixels.
The Samsung Galaxy S3 mini I have is 800x480 pixels
The full Samsung Galaxy S3 is 1280x720 pixels.
The latest top of the range Samsung Galaxy S4 is 1920x1080 pixels, the same resolution as my 24" computer screen at home.
So if you are going to use the internet a lot you may want to consider getting a better phone for a better internet experience.
I know you have only just got the phone, but 320x240 is just not going to be big enough to display much information from the internet. It also has a slow CPU and not much memory.
One of my relatives just got a deal from Argos for a free phone (Samsung Galaxy Fame) and 50 minutes of calls, unlimited texts, and 250Mb of data, all for £10.50 a month.
The Fame is not the greatest phone, but the screen is twice the resolution of yours. The Fame also has a lot more memory than the Galaxy Y (4Gb as against only about 300mb of memory in the Y)
Note also Samsung phones run software called Android (like computers run Windows) and the Samsung Galaxy Y that you have runs a rather old version of Android.
The Samsung Galaxy Fame runs a fairly recent version of Android (4.1.2).
The most recent version of Android is 4.3
Because smartphones are like computers then the version of the software they run becomes ever more important, as does the CPU they have and the memory they have, they are mini computers.