I have been organising my clubs kit for the last couple of years.
The first time I was volunteered to do it after mentioning I knew someone who ran a clothing company dealing with sportswear and hoodies etc. and thought he could do a job. It turned out to be a massive pain in the (No Swearing Please) as he sourced all the stuff cheap from Pakistan and they run their embroidery machines at about 140%, which leads to pretty shoddy work. Not only this, but we had to organise a bulk order for a whole club. Anyone who has done this before will no what a ball ache it is with everyone wanting different things in different sizes with different sleeve lengths etc. Of course there were lots of issues which were not easy to sort out.
I vowed never to do it again but was again volunteered to remake the clubs website as the our old one was pretty embarrassing. Again I had mentioned that I knew of a cricket club template website (hitssports) that my old club use and was volunteered for it. A couple of months after I had made the website, Hitsports announced a partnership with Serious Cricket to provide integrated club shops as part of the website. This meant that our club website now doubles as an online cricket shop and we get a 5% cut of all sales.
To the point, Serious Cricket also offer team wear. The team wear is great quality and Neil Rider who works there is very patient whilst you are sorting out your logos etc with him. The only criticism I would have is that there are only two designs of playing kit, both of which are pretty bland but the ease of having a club shop which caters for orders individually as and when people require them far outweighs that.
As far as I am aware, you don't need to have a website with integrated shop to set up an account for your club with them, they can produce all your team wear and give you a section on their website for all your clubs gear.