Hi Noob,
I can imagine how frustrating that could be. What you have is a site that offers a service, and that service itself will generate a ton of links. So the question is how do you attract both buyers and sellers (listers and lookers) right?
In cases like this it may not be the best to focus mainly on building backlinks, rather focus your efforts on other marketing avenues. This could be email marketing, community type engagement (Local Area Websites, Industry Specific Websites, Charities), print (Newspapers, Magazines), Radio, Online Advertisement (Facebook, Twitters, Google, Yahoo).
Without knowing exactly what type of classifieds you plan on running I can't be very specific. However, I will say the "classified" type website is nothing new and as I'm sure you're aware you're up against some pretty big names (Craigslist, Ebay, Angieslist, LocalAreaNewspaper/classifieds.com) Which means if you're going to fight in this arena you should be doing something they aren't doing, or whatever they are doing better.
This type of website is one that is very good at generating its own links as many "sellers" will post links to their items on Facebook, Reddit, Instagram, Twitter and so on. You could take advantage of this to get a main link to your domain by offering new posters a quick code grab which includes a link to the specific product they just posted along with a link to the site itself.
Of course if you're talking personals that is a different animal in where you approach people but the theories are still the same.
The things you can do in either case is to focus on making sure the site is as easy as possible to use for both listers and lookers. They both should have a great experience. Make sure they are completely informed about fees and how the service works. Along with that offer lots of back end features that allow both sides to ease of use, in the areas of tracking and searching.
In all cases how these sites stay around by being relative. Ebay is still around because people still buy stuff from there, despite the ridiculous fees and issues sellers have dealt with over the many years. If eBay were to lose sellers that would have a direct impact on lookers and vice versa. Keep both sides happy, you need them both.
Hope this helps in some way,
Don