Own 3 Bromtons, one with a rack. When you don't have a rack you can sometimes miss one if you need spill-over capacity. The front pannier system is so much better you use that til its stuffed, so the rack ends up hardly used - but good for pizza.

You can use a backpack as you described when you need more capacity but then it can be a bulky item to put in your pannier. I use a small spill-over capacity one.

When you have a rack, its always there adding weight and it moves the low-down light from nearer the center-of-gravity folded to further out so makes the bike even heavier, it is noticeable weight and the rack and roller wheels knock your calve area a bit more than without the rack.

So I'd advise fit the rack only if you are sure you are going to be pushing it folded on decent surfaces where the rack then makes a decent trolley type, otherwise save on weight and cost and don't have a rack.

The T-bag is bigger, you can do decent shopping and touring type trips with one, but the C-bag has more compartments for more a daily living type. I initially used T-bag when but now use C-bag and the above spill-over capacity trick it does me for a fair amount but I have the racked Brompton too for touring type situations. I'd say go for C-bag unless you're sure you are going to be basically using the Brompton to do all your shopping. I did all my family's shopping on Bromptons for some years and the T-bag with a big throat easily swallows more and can be overstuffed and keep the goods internally better. One common issue with T-bag owners is the volume attracts just keeping lots of stuff in it because you have the room, so tends to become a little tramp like.

I prefer the S-bar because its a lower body position for less wind-resistance which matters more if you're doing higher mileage and if wind is an issue where you are. I cut the handle off the frame and used some laces to make a soft handle as otherwise the plastic handle would pinch the brake cables on the forward-leaning stem. The only downside is a C-bag on the S-bar the bars have to be square so the levers aren't in the way as the bag drops into the block.