What are typical requirements for getting approved for an options account with a stockbroker?

When I opened my options account it was about all three factors you mentioned. The broker will need to be satisfied that you cover losses and have the disposable income to trade options. To get experience they probably approve you for covered calls and calls at first. Once you gain the experience then they will approve you for puts as well as trading naked options and other strategies. If you want to get into risky option trading they will require a margin account. So, expect to get approved for basic option trading at first and you can upgrade later as you get experience. This is how it went for me although I refuse to trade on margin so I can only go as far as selling cash secured puts as a strategy.