I think a good quality bag is important - I have a Kapoochi Vintage and an Storksak - both quite expensive (got the Storksak half price tho) Both bags have been used a lot and still look as new with no probs - friends have bought cheaper bags that have fallen apart very quickly.

I like a purpose built bag. I love both mine and I like having lots of compartments so I am not digging to find things. I also find the insulated section important now we are on solids. If you want to use a regular bag - google the Pouchmiss - it is an insert for a regular bag but with all the features of a nappy bag. I am planning to buy one to use with my massive handbag collection