Hi, I got a website, I wanna add a web contact form and a auto response email handler which will go to inbox. Do you guys have any idea?

I think that you need to have helpdesk software.
kayako is the most popular one.

There are tons of tutorials online on how to create a contact form. It really depends on what platform you are developing it on (.asp or .php, etc).

For the autoresponder, you can hard code that in as well, or create an autoresponder with your email account. For example, setup an email account that is only for your form and once someone fills out the form it will go to that email account, which will then shoot off the autoresponder. This is simple and gets the job done. If you need to do more than that then you will have to either custom code it or signup for an autoresponder service. Here is a list of autoresponder comparisons.

Well if it just starts, you can use the usual contact form...

But when it starts to grow, you can consider help desk software like kayako, it is very good and popular one

Is it free or paid solution? I have heard several times about that