This is mainly an issue with the launch models, the Xenon and Zephyr. Avoid those like the plague. By the time they got up to the Falcon the fail rates weren't problematic, the Jasper is actually good, and the Slim models are good too.
If you're going to local shops for the system, you can glance at the power socket to identify the model:
From the good systems I think the Jasper has the most modding options, the Trinity has some acceptable options, and the Corona isn't the best for modding. Keyword there, think. I haven't modded any 360's, I'm just reposting some hearsay which I may be misremembering. Hopefully somebody pops in with some better opinions.
You can expand the HD on every 360 model. They just use laptop drives in a useless enclosure. I think the max official size is 320GB, but I've heard of people slapping 2TB in there. Going over the official limit might get you banned from Xbox Live (who cares...).
Yes.