Yes, we're obviously biased against Shopify as a solution, but the main criticisms of it stand up.
If you make your own site on a popular platform such as WordPress, or get your host/designer to make it for you, and get your own hosting, then you're in full control.
Your design and hosting aren't permanently tied together, so you if you need to reduce cost in the future, or upgrade performance that's no problem and you'll have plenty of choice.
Likewise you can also start by building the site yourself, and then get a professional to take what you've made and take it to the next level in a couple of years for example, once the business has taken off.
To do that with Shopify you'd have to start again, so it doesn't scale in the same way. The ongoing costs for what you get are also really quite high.
WordPress + WooCommerce would suit an image/detail heavy online shop for selling t-shirts very well I think.
I'm guessing by 3D t-shirts you mean dye sublimation printing like this:
http://www.amazon.co.uk/Cody-Lundin-Compression-Captain-Avengers/dp/B013YPHNRU
I don't know of any dropship/all in one t-shirt printing options that do this.
I'd recommend some good quality UK eCommerce hosting. You can get WordPress installed for you, and add WooCommerce. You can then also get an SSL certificate installed for you for SEO benefit and to improve visitor confidence.
Some hosts will provide a management option so you can have it all set up for you with some dummy pages to build the site yourself, or you can have the base website made for you as well.
I imagine Printerest and Instagram would be good channels to drive traffic as well, depending on your target market and audience.
I hope that helps.
If you have any questions feel free to get in touch.
All the best,
Dan