Transfer Customer and Product data from Old to New website

[onlinestore23]

I am running 1.7 version of Magento on Website1.com. I am planning to create Website 2, install 1.9 version of magento, then install many new extensions and once that is completed I need to transfer all customer and product data from website1.com (OLD) to website2.com (NEW)

I am just not sure what exactly shall to transfer
Should I transfer full database from website1 (OLD) ?
What files should I transfer ?

The way I was thinking of doing it is.
1. Make a copy of my website 1 and update it to Magento 1.9
2. Then instal new templates, extensions and adjust settings. But it will take me 2-3 weeks to make changes on the new website. Once finished how can I transfer most latest customer information from Old Website that were created during the period I will be developing the New Website? Before I launch New website I want to have up to date information from Old website, missing 2 weeks of orders and customer data is not good.

All I really need is customer data and product data. I don't need settings, extensions, and so on.

[Brent W Peterson]

You only need to do the following steps and all your data will be in the new version of Magento:

1) Make a database backup of your current live site.

2) Get the newest version of Magento in a test enviroment 

3) Restore you database to your test enviroment and point your new version to this new database.

4) Run your site, it will upgrade your database and all your customer data will be there! 

It is like Magic but with less work.

After that you can install you modules and your theme.

[cannonballdex]

Will this work upgrading from 1.3.2.4 to 1.9.2.1 database?