There are quite a few usability concerns with option one which I would caution against:
You are making the assumption that users can understand that the word prepaid and it has a whole list of options namely credit card, debit card and netbanking. The user is left to make an assumption about the word prepaid entails which can lead to many interpretations. Also if he goes with an incorrect assumption that the service does not support debit cards you might lose a particular customer as well. The customer might also think that Paypal might be a prepaid option and be surprised to find that its not an option leading to increasing frustration.
Increased number of interactions : The user on selecting your prepaid option would then need to choose which prepaid option which is an additional cognitive load on him
Increased cognitive load to recognize what terms mean : This partly goes back to my first point where the user is required to understand what Prepaid or COD means (I would get what COD means but if I asked my father, I am afraid he would not understand what it means)
The advantages of option Two are
Easy visibility of all the options : The user is aware of all the options straight up front with no confusion about what each term means.
Quick access to the desired payment option : This ties in with the previous point but with the option of showing all the payment options, you allow the user to make a quick decision and get to the payment option desired.
Now coming to whether icons are needed ?
I would say yes since your icons provide a quick visual indicator of the payment method as the user scans from left to right and the labels will serve to confirm the users understanding of the icon in case there is any confusion. To quote this article
All user interfaces make cognitive demands on users. Users must master
special rules of system use, learn new concepts, and retain
information in short-term memory. They must create and refine a mental
model of how the system works and how they should use it. Successful
user interface designs must respect the limitations of human cognitive
Tests showed that visuals are processed 60,000 times faster than text,
and people could remember more than 2,500 pictures with at least 90%
accuracy several days post-exposure, even though subjects saw each
picture for about 10 seconds.
The inefficiency of text has received particular attention. One of the
reasons that text is less capable than pictures is that the brain sees
words as lots of tiny pictures. And when we read, most of us try to
visualize what the text is telling us. We essentially create icons
inside our heads.
Using icons or symbols on a device serve as aids to memory, thereby reducing cognitive load since we can process icons and symbols
much quicker than we can read text.
That said, only using icons is not a good idea as this UX Myth article talks about
The Microsoft Outlook toolbar is a good example: the former icon-only
toolbar had poor usability and changing the icons and their
positioning didn’t help much. What did help was the introduction of
text labels next to the icons. It immediately fixed the usability
issues and people started to use the toolbar