Unfortunately, there are not easy answers to how much they want to see to feel satisfied that you won't need to rely on public funds. It all depends on so many things, such as where you'll be living, etc.
If you're in doubt, is there anyone here in the UK who could co-sponsor you?
Also, i believe that your baby will be considered a UK citizen when it is born, and since he is a citizen as well, the only person in your family that *won't* be able to claim public assistance is yourself. So it may not be so bad really!