Children's Pythons are part of the Antaresia genus ('family'). There are three species in this group which would be equally suitable (Children's, Spotted and Stimson's). These are all very similar in terms of care, similar in size (Spotteds are slightly larger but still small snakes) and the main differences are colours, patterns and prices.
One of these three is definitely going to be your best choice. Anything else will be much larger and/or more difficult to keep, and the alternatives still need to be fed rats, mice or chickens (the ones which will be suitable to feed chickens are much larger).
The closest things to Garter Snakes in Australia are tricker to keep and generally get fed live fish. Definitely not something you want to start with (Garter Snakes themselves aren't idea first snakes).
Snakes aren't friendly, cuddly animals like cats, dogs and rats. They're fascinating and beautiful, but they are predatory and can't be fed a disguised diet like tinned cat feed or dog biscuits. If the idea of being honest with yourself and the reality that you have a predatory animal as a pet is unappealing, please don't get a snake. If you want to admire the beauty of a unique animal and embrace what it is, then you may enjoy a pet snake. Keep in mind that a kitten with probably bite you, a puppy will probably bite you, and a snake will probably bite you at some stage too. It won't hurt anywhere near as much as a dog or cat bite and won't have the same risk of infection, but it sounds like this may scare you.
Perhaps it's worth asking you why you want a snake rather than a dog, ferret, rat, budgie, fish or pot plant. There are plenty of good answers but they don't apply to everyone. If someone says they don't want to feed off dead rats, it suggests they may be better suited to something else.