I'm going down this route too, but I'm probably taking the longer less costly way.
The easiest way has probably already been mentioned in having some type of store front setup by way of inksoft or Deconetwork or the likes - Unless you're deep into this though the cost is rather high.
The benefit here is a total integration and a standalone piece of software to take care of fulfilment, costing and a host of other features - Probably shipping integration too which I didn't look into with either of these. There were some problems in these that didn't entirely work for me either, but that's more a local issue than the respective software themselves.
The other alternative would be the myriad of storefronts like Big Cartel, Volusion, shopify etc etc etc. One of these I did seriously look at which may be of use to you is ECWID back-end to a facebook store. ecwid.com. They have a free setup whereby you can build a facebook store in your clients current facebook page - Most people or groups have one of these pages anyway so it's a sensible option. ECWID clips the ticket on the way through but they handle all credit card processing and provide the tools to set it all up. It's a very simple system and if you decided to take a subscription to have more than the 10-15? products the free setup allows, the pricing is pretty reasonable.
Of all of them, I thought the ECWID solution was best bang for the buck and reasonably simple all round. So it really is worth taking a look there.
Myself, after all the looking and testing decided the Wordpress/Woocommerce system worked for me and where i want to go. It ties in with the back end accounting system I use (Zoho suite) so I can keep track of inventory through sales, I also pay for an add on that splits the transaction so I immediately get my portion of the sale of the item, and the remainder goes to the client hosting the website/facebook page.
I just didn't want to deal with taking the whole sale, working out the profit after transaction fee's, having to pay the store owner, working out invoicing for him and back/forth. This way I just get my money and whatever the other guy does with his share is his problem.
Selling the item online is no problem, producing the item and delivering that item is also no problem - It's that void of paperwork between two parties to deliver the item to the end user is what I found an unnecessary problem, so I took a longer route to cut this problem out.
Shipping is also handled through the back end Zoho suite. I'm not double handling anything or copy and pasting shipping addresses.
Essentially an order comes in saying what store it's from, the garment, garment size, garment colourway, gives me an item code that matches a visual/proof I have, gives me a shipping address, and also gives me the pre-determined amount to produce and send the item.
--------
I have quite a big picture of where I see myself heading though. So, whatever I'm doing now, I'm looking to take the route that is a simple system to follow, but chews up the least amount of profit for when I have 200-1000 of these stores.
At the moment I actually have no stores!
The reason for that though is I want to be entirely confident that the procedure is down pat and solid. I wan't to make sure the system works and functions as it should so I can hand it over to someone else to take care of, and we're not all going to be buried in paperwork and some confusing and ropey garbage.
It probably reads confusing and ropey already - It's not though. I found when I was getting into it and looking through these systems is they can grow out of control if you just dive in and don't look at every step. I've tried to account for a bunch of variables - Half of them I've probably forgotten anyway, but I've ended up where i am through realising a lot of pre-made systems simply wouldn't work for me as I was looking at them or trialling them.
What you describe though is what I'm doing. Producing transfers to hold in stock. Someone orders and I just order the garment, brand it, ship it out. A LOT of small quantities. 1 of this, 1 of that, 4 of those, 25 of something else. At the moment I just handle it manually which I've made easy enough. But the goal is to have it all online through multiple stores so it's simply a case of a client logging into their store, filling a shopping cart of whatever they want, me receiving an email order, processing it, and moving onto the next one.