Selecting the right e-commerce software is an important decision and one you should not take lightly. You're likely to be working with the same shopping cart software for years to come and factors like ease of use, maintenance and support should all be considered.
We typically use Woocommerce and Magento to design and develop on. There are others (Squarespace, Shopify) available but these often require you to lease the software whereas Woocommerce and Magento allow you to own your own eCommerce website software.
Magento
Magento shopping cart software is vast. It has many configurations and settings and because of this it can be overwhelming to the average web user. Magento has excellent support from third-party plugins and, since the passing of ownership from PayPal to Adobe, the releases are becoming more worthwhile and effective. Magento provides a very large, professional set of tools to create your e-commerce website but can be costly to maintain due to the fact it has such a large number of moving parts. Development support is widely available.
Woocommerce
At the time of writing, Woocommerce is the market leader with close to 30% of all shopping websites on the internet using it to process their orders. Woocommerce is reliable, light and can be easily customised. One downside is that there are a lot of sub-standard plugins available. The market leader is also often targeted for website attacks. This can be mitigated by strengthening the security and adding fail-safe mechanisms to thwart hacks and stop them. If it's protected well, it's a great solution and you'll find no shortage of developers willing to support it.