Hi Will and welcome to the site
Good luck with your trading shed, it's a fabulous resource once up and running. I don't manage our shed but help out with the sessions.
We use Codnor for our bulk orders, including things like seeds - they offer most of the Mr Fothergills vegetable range, and also I think another company on the same terms but they only have a web catalogue whereas people can browse Mr F's catalogue in the hut or take a copy away in order to place an order.
On browsing our association blog (see my www icon) I also note that we're exploring using Acorn supplies in Bingley W Yorks.
Other lotty associations use Kings seeds.
Make sure you buy in bulk if possible to maximise reductions.
We stock canes, slug pellets (controversial), glyphosate, full range of fertilisers, seed spuds both to order and ad hoc, onion and shallot sets, a limited range of pea / bean / broad bean seeds at appropriate times. Also fleece and weed protection, which I think we got in 100m rolls of t'interweb.
We also order in manure from a local supplier - aminopyralid free - and ask members to pay per barrowload.
We have seasonal advice available - copy of John's books and the monthly growing guides from here.
Pitfalls - over-ordering on things which date (e.g. some pesticides which are withdrawn, or seeds which won't keep). We've stopped stocking too many packets of seeds as the shed is a little damp and they weren't selling. This is a really difficult balance to achieve as you want to order sufficient for discounts yet not so much as to have to write off stock. It will probably take a couple of years to get a feel for your throughput. Perhaps get people to place orders as much as possible?
We have our shed insured under a trading policy - it's a difficult one but we decided that as it's a wooden shed the risk was too great.
Another thing to consider is whether you want to offer any subsidiary services - this will probably depend on whether you have an association or just the trading shed. We have joined the RHS Affiliated scheme, which offers the gardening advice line, access to reasonably priced insurance policies for events etc, and you can buy a card for £10 which gives free access to all RHS sites for two people.