All trades inform the Recruiting System of their requirements for new recruits in periodic cycles. There's always a demand for infantry (among others) because its a large trade and the machine has to be fed to maintain numbers.
Choice of trade doesn't dictate speed of selection and the offer as much as suitability for chosen trades.
There are no simple answers to your question that will give guaranteed results.
Other answers may offer different perspectives, your mileage in interpreting them may vary.
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