Since I have never used any PHP frameworks, I’d like you to suggest me some.
My main objective is writing a fully functional penny auction script, something similar to swoopo.com and bidhere.com.
While at it, please leave reasons why you think the particular framework is best suited for this job.
I would recommend reading this question when it comes to choosing a framework.
https://stackoverflow.com/questions/2648/what-php-framework-would-you-choose-for-a-new-application-and-why
There is not a specific framework that is better for one site than another. It depends more on how you want to implement the code.
However, I would recommend that you write your own small framework. This is what I have done and it is very beneficial:
From there you can copy your framework and use it on future websites. Also, when doing freelance work you can advertise that you fully coded everything, which may equal more money.
When I was looking into frameworks I did not like how any of them displaying templates and went the route of making my own framework and definitely am happy that I chose to. No longer do I have to worry about settings that I will never use. (This should also result in some faster speeds, but am not completely sure about this.)