Website Migration From CPanel backups to PHP/MySql E-Commerce Solution

I have recent CPanel backups (a [login to view URL], a [login to view URL] and a [login to view URL] file) of the databases which comprised my e-commerce website. The site is currently not hosted on a server. The site was built on a shopping cart platform called SquirrelCart but I want to migrate the site over to Magento or some other PHP/MSql solution and get it up on another server or perhaps to a WordPress platform with WooCommerce plugin which is another viable alternative which has been suggested to me. I'm open to any platform as long as the demo is functional and the price is right. I need to have a shipping calculator and to integrate PayPal processing as well. There are fewer than 100 items for sale in the store database and I would like to maintain the URL structure of the original site. I have never counted the number of customers or orders (each of which may number 1,000 or more) but need to maintain those archives as well although not necessarily on the new website. If it keeps the project within budget, a separate database could be an option. The main thing is to maintain smooth navigation and alignment of the target site. I have found snapshots of my site up on [login to view URL] which would offer a template of how the site should look. I can provide access to the databases and domain name via PM. Please note that a working demo of at least 2 or 3 of the times should be made available.