Maybe start out with a smaller bag? I think most people tend to fill whatever size bag they have?
I've always carried small bags compared to most of the mums I see at play group with super sized nappy bags.
When DS was a baby I carried a tiny woman's handbag, 1 bottle, 1 cloth nappy with a few cloth wipes wrapped inside, 1 muslin.
During PT I sized up to a woman's over-sized handbag, potty or toilet topper, 1 pants, 1 pair socks, 1 shorts, 1 t-shirt, bottle water, handy pack of tissues, travel pack wipes. I could definitely have fitted more in that bag - ie the things I carried for him as a baby.
Later in PT when DS would stand up wee, I ditched the potty and carried a small plastic drinking cup and returned to my small handbag, so cup, travel wipes, travel tissues, 1 pants, 1 shorts. Although I did keep the potty or topper in the car for emergencies it was not always close by.
I've always taken snacks in very small tubs and never taken toys. The only time I would take something would be a small book if we went to a restaurant (then I'd take his cutlery too), otherwise I'd just assume we could find something to occupy him out and about wherever we were. A long wait in the pharmacy I'd just hand him a sealed pack of vitamins to shake or later walk around the shop counting bottles or naming colours whilst we waited.