I am awake and still thinking about delis xD and I feel like this is quite dependent on the type of "deli" you are.
E.g. quite a lot of people here are talking about food to take away and eat there and then i.e. not to put in the fridge. I think round where I am that's not really a massive thing, I suspect because of the age demographics of those shopping in the deli's.
Round here most are definitely selling posh sausage rolls, cheeses, cold meats, bits and bobs like quiche and some good olives (though not the giant vats you can drool over in France), they'll generally have a collaboration with a local baker but obviously there's a high risk of waste there, particularly at first.
They'll have some interesting jars/sauces etc and depending on the place they may sell some fresh veg that you might want to pick up.
They're not really in the market for work lunches or anything round here. Some will have the odd random mug. All the ones I can think of here are rural-ish. Some veer more into farm shop, some into butchers, the odd one has a bakery on site and swings heavily in that direction. The lean generally depends what they started off as. Because they're rural it's probably more worth them having a wider variety of produce. If you were in one of the market towns and you have an artisan bakery two doors down there's probably not much point trying to sell bread! If you get your artisan bread delivered from the bakery 10 miles away and there's no decent bakery nearby you're going to be in a better position from that POV.
So I tend to think you need to have a think about what your customer numbers are like, what your catchment area is, what else is within your catchment area and go and visit it and see what they appear to be selling lots of to consider if it's a speciality on which you are unlikely to complete or something on which competition may win you customers.
I'd be doing quite a lot of that by literally just having a chat with customers as they come by and if you possibly have time making some notes on it so you don't bias your data too much by what you remember.
I think what's going to be successful will be massively determined by the rurality of the area, the demographics of the local populations in terms of all of age, background, amount of money etc, and what else is in your catchment area.