As for the second adapter, it really depends on the make/model of the extender. However, to guide your choice, it really depends on what you need in the bedroom.
The adapter connected to your Main router obviously has to transmit and receive wirelessly. That's why you're doing this: to communicate remotely and wirelessly with your Main router.
The second adapter must receive wirelessly. However, it doesn't need to transmit (repeat, pass-on, extend to you) whatever it receives wirelessly. It can just pass-on whatever it receives through a cable.
As for what you need in the bedroom, as Jim mentioned, what will be using the signal from the second adapter: 1, 2, 4 other clients? If it'll just be 1, connect that client. 2 or more, connect an AP. 2 or more wirelessly, connect a wireless AP. Also, think about an future plans.