SSP's and Self Serve are two related but very different concepts. First, let's look at SSP's (referred to as both Sell Side and Supply Side Platforms - both would technically be correct).
SSP's provide technology for publishers to sell their website inventory to advertisers (who use DSP's, or Demand Side Platforms). SSP's generally run their own ad exchanges, just as ad exchanges usually have their own media buying and selling technology. However, SSP's allow the publisher to tap into multiple ad exchanges, thus giving the publisher more inventory and monetization opportunities.
The assets (ads, creatives, destination URL's, etc.) are hosted in ad servers. Publisher and advertiser ad servers exist. The former tap into SSP's in order to sell the inventory; the latter tap into DSP's in order to access that inventory and push the creative assets.
Self Serve Platforms are basically ad servers, connected to some SSP (or DSP, if you're an advertiser) that allow the publisher to go in and manage or traffic ads. That is, a publisher would manage how and to whom they would sell their website inventory (consisting of container tags on the website that call the creative assets) but they can also site-serve creatives (or place creative tags and tracking into those slots themselves, instead of calling those tags from DSP's).
In display and programmatic advertising, you can either have an Ad Ops team traffic your creatives and manage your campaigns (thus, Managed Service) or do it yourself with your own team (thus, Self Service). Not every ad serving solution is available for self serve.
All self serve solutions must have some sort of oversight, or the users will upload bad or legally non-compliant creatives and cause all kinds of havoc that can break user experiences and bring on lawsuits. Thus, either 1) the solution's QA team is monitoring and rejecting creatives, or 2) they outsource it to India or Russia, or 3) they use automated technology to do the heavy lifting and then QA anything that's ambiguous. Usually, it's a combination of 1 and/or 2 + 3.
Ultimately, the platform you choose will have to do with who specializes in the best types of media for your goals. (Video, native, rich media, etc.) Of the platforms that your Master New Media link lists, AdReady and AdRoll are two that I've encountered. Both are legit, though AdReady is the one I've dealt with more, and would recommend running with, because they are used by some very big agencies and brands.