Why were Curiosity's first Mars photos black-and-white, low-resolution, and surrounded by a white border?

It's a matter of file size and transmission time. As you pointed out, these are the first photos from a mission that has just landed (and which had a huge potential for failure, given the complicated and completely automated landing procedure necessary to land such a large robot).

Mars is a very long way away, and even with a very powerful transmitter and a highly-focused signal, the radio signal reaching the Earth is going to be rather low in power/amplitude. There is also a lot of radio-spectrum noise coming from all over space. Together, that means that the signal-to-noise ratio is going to be pretty low compared to short-range terrestrial transmissions. There are ways around that, of course, but they all include a rather severe restriction on the data bandwidth. High-resolution colour images take a relatively long time to transmit successfully; low-resolution grey-scale images are much, much quicker, and for an initial situational assessment, they are good enough. The big full-colour images will be coming, but they can wait a while.