I found Paperform.io to be a straightforward and easy way to add products and checkout to my site with a complex order form. Foxy can do it as well, and is more powerful in some ways, but it took less effort for me at Paperform. I’m not sharing this as a promotion for them, just as a user who just went through the process of picking a third party form tool to embed.
If you plan it right, you can easily export your Products CMS as a .csv, trim it to the relevant fields, and import it to Paperform, and you can built more complicated interactions from there with Zapier if you need, but Paperform has everything needed to catch an order and process payments.
If you do use them, using this referral link to get there will save us both 10%, but this is a genuine testimony not a click-fishing response.