When I do lightweight shoots I take my lowerpro messenger style camera bag. It has removable padding but once the flap is on it looks just like a regular messenger bag. Won't fit much in it though. I can fit a Pentax 6X7 medium format (which isn't exactly small) with a 110mm lens in it along with a few necessities like a notebook, little credit card holder and my phone. That's about it.
Or, I can fit two smaller cameras, like my Pentax 35mm and a Konica Rangefinder along with the necessities.
These lowerpro bags are really cheap too. Look at Amazon!
The bag I use the most is a canvas messenger from ASOS, I dont think they sell it anymore. Comes with a nice soft removable shoulder strap and tote style carry handles. I shoved in a thick layer of adheasive backed egg crate foam and it works very well. It got really grungy at one point, but it cleaned up well. I think it cost me $12, the foam I had lying around. Not water proof though, I will probably wax it one day when I get around to it.
A good quality bag designed for cameras will almost always be better protection. But it does advertise "camera". A thief is likely to steal first; then look closely at what's been stolen. I got the impression that you might be in locations where that might be an issue.
I've used a short length of heavy mailing tube for lenses and small cardboard boxes inside a bag with a flat bottom. Sounds tacky, but it works as long as it's just 2-3 items in the bag.