Need advice on creating and selling merchandise

Hello all. Firstly thank you to anyone who can offer me any advice here, it's greatly appreciated.

Cutting a long story short I want to make merchandise for a small niche that I'm very passionate about. Right now most of the merchandise for this niche is kind of lame so appearance wise I will have little competition. The issue is production and selling. Now, I will advertise the merchandise through my website (powered by wordpress), facebook pages and Instagram account. They will all get pretty reasonable traffic for a small niche site. But I'm not sure about how I should go about production. My customers will mostly be in the USA, UK and rest of Europe. I have the designs nearly ready to upload and I figure the best way to sell will be choosing something like Amazon Merch, Teespring, Café press or another fulfillment website to have the merchandise produced and sent without costing me anything. I was thinking to cover all my bases, potentially uploading my designs to more than one of these websites to increase my exposure but not sure if that's a good idea or not. Similarly if I setup an ecommerce section on my website, could I simply take peoples payments and then place their order through a fulfillment website?
Understand that's some tricky questions but TLDR I have designs, an audience to sell to and need to figure out the best way to produce the merchandise and sell/ship.

Thanks again.