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If the subdomains are related to the root domain, then subdoamins is the best answer.

There is not any direct actin you can take other then to contact the source of any spammy links and request their removal. Indirectly, you can earn quality links to dilute the bad ones in your profile. Most sites will have some spammy links to them. It is perfectly natural. The question is what percent of the links to a given site are spammy.

Stay away, i think we have all been tempted once, but it is not worth it

I prefer the second site but I would be careful about using lots of links in your footer.  It doesn't look good and is seen as a negative by some search engines.

A great test on those paid links would be to change the directory listings to point to another website or domain that you own which has been ranking pretty steadily over the past few weeks.  If you see a decrease in organic rankings on that site as well, then you'll know for sure that the paid directories were the problem. If the directory listing was cheap, then it might not be worth your time - you'll need to weigh the pros and cons.