These plans are in flux. At a core level (heh), we nee to have libraries ported first
anyway. So we're doing that now. Jil, StackExchange.Redis, Dapper, and Sigil are up on NuGet and core compatible today (some as pre-release). Others like Exceptional are just pending some RC2 goodness to release, and I'll be starting on MiniProfiler after that. We'll likely post other internal tools to .Net Core and start heavy testing in the RC2 time-frame.
Will we run Stack Overflow on core? Probably not for a while. I was asked exactly this in a recent On.Net interview at the 24:22 mark; you can listen here for reasoning: https://youtu.be/DJn8-Psznsw?t=24m22s