1. To attain ranks above Member, you'd have to earn some number of merit points. Merit points would be awarded in a monthly vote on best posts of the previous month, with various measures (TBD) to prevent gaming of the vote. Winning merit points might also come with a BTC prize.
This sounds like a good starting point but the gaming issue could be very difficult to address.
2. Create or designate some sections as "serious discussion" sections, with no signatures. In those sections or maybe in different ones, also have poster restrictions such as Member rank or above only. And/or allow topic-creators to set these restrictions on their topics, similar to selfmod topics.
The no signatures part I don't really like as that doesn't seem fair to advertisers. They, in theory, pay for quality posts in serious discussions that are far more likely to be read. Allowing topic-creators to set restrictions is a good idea and maybe making selfmod the default so people take responsibility for keeping their own threads clean.
I agree with hilariousetc/co's suggestion to offer upgrade memberships that give higher member level signatures. This would go a long way to reducing account farming and people spamming their way up the ranks.