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Your chickens may keep the pests down in your garden but they will also scratch up and otherwise murder your garden plants...so chickens in the garden won't be a success.
Plan to get breeds that will provide consistent and longevity of lay instead of just getting breeds that look pretty and breeds known for hardiness so that you can keep your three a long time before having to deal with age/health issues. If you are only getting three and you want them for egg production, then you might want to get breeds that are docile, hardy and provide good egg to feed conversion, as well as good foragers.
Black Austrolorps are a great breed for this, as are RIR and Barred Rocks~and they are all still beautiful breeds to look upon. All the chickens I've had of the three listed were sweet, healthy, beautiful and laying machines.