ECommerce software suggestions
Hello 84wTn !
I would steer away from Magento because its a very heavy resource intense eCommerce platform. With that many products, would need a VPS or Dedicated server to run it. There are many Open Source software eCommerce solutions out there that you can use with low costs and less server problems. See the list below.
PHP Point of Sale
I recommend checking out Prestashop, OpenCart, or osCommerce. These are the most popular and have many plugins and compatible merchants available. The difference between them is how the Administrative panel is set up. Some people prefer one over the other. You can demo them at the following links.
If you have a cPanel hosting account with someone you can install these for free through Softaculouos. Or you can download them fro the website and install them manually.