Do backlinks have to be to just your domain or do pages count?

[Jake]

You should mix it up, logically a link would go to the most relevant content page.
Actually the maker of one backlink automation tool recommends in a webinar to not link to the home page, do to them being much harder to eliminate, at a later date than inner links. Since Google began actively penalizing sites for spam backlinks and not just ignoring them, it's best to be prepared to remove questionable links should you receive the dreaded "Unnatural link pattern" warning from Google, in order to avoid being de-indexed for 6 - 12 months.

You can always change the uel of an inner page to 'shed' any backlinks to the address, while your pretty well stuck with home page links, It's better to link to yourdomain.com/index.html so you could change the index.com part if there is a bad link problem.