Registering in webassessor.com for salesforce certification for the first time
Choose customer initially. Partner is for special circumstances like a company that is an ISV or consulting partner for example, and employee is for an employee of Salesforce directly. If they ask for a company name just list n/a for now. Later on if you become a consultant the company name field will become important for bubbling your certifications up on the company's AppExchange profile.
The opt in for verification is in reference to the verification site (http://certification.salesforce.com/verification). If you opt-in, you'll be publicly visible on the site if someone enters your details.
Training related additional info: Make sure to check out Trailhead if you haven't yet. That is an indispensable resource for learning. Additionally the documentation online at developer.force.com is of course very useful, particularly for getting specifics of a class or method.
Trailhead: https://developer.salesforce.com/trailhead DeveloperForce: http://developer.salesforce.com
I got the Answer for my Query after raising a case with Salesforce. I am copying the reply from Salesforce official on my case to below as it might be useful for others in Future.
"By selecting SFDC Partner, your account will be linked to your employers account. You will also be added to your Partner Community or AppExchange listings. SFDC Employee is for Employees of Salesforce and SFDC Customer is for people who don't fall into either of the other categories. For you, I would recommend SFDC Partner.
All Certified Professionals are provided the option to share their certification information and make their certifications available on the verification page through the 'opt-in' verification box. If you select yes, others can search for you by name or email address and view the certifications you hold. The certification verification page will list your name, location, all of your active Salesforce certifications, and the date you became certified. By referring to the certification verification page, customers and partners will be able to easily validate your expertise (certification.salesforce.com).
For additional information about the Certification program, please visit our knowledge base at http://certification.force.com/pkb"
Thanks anurag-bhardwaj for your advise on the same..