E-commerce Integration into Existing Website

I already have my website designed and live, with all products uploaded and laid out. Currently, purchases are processed via an enquiry form, and I’m now looking to convert the site into a fully automated e-commerce experience.
I’d like to implement:
Add to Cart functionality
Streamlined checkout process
Shipping calculation and integration
Secure payment gateway setup
Apple Pay integration
Afterpay integration
Order confirmation emails and basic automation
The goal is to create a seamless, elevated checkout experience that makes purchasing simple and intuitive, encouraging customers to complete transactions directly through the site rather than submitting an enquiry.
The design and brand aesthetic are very important, so the checkout needs to feel cohesive with the existing look and refined in its execution.
Please include:
Your experience with e-commerce integrations
Platforms you specialise in (Shopify, WordPress/WooCommerce, Squarespace, Webflow, etc.)
Estimated timeframe
Examples of similar work
Looking forward to working with someone detail-oriented who understands both functionality and design.

Images attached of the similar design aesthetic.