After owning a fat bike for a short period I’m starting to come round to semi fat for the grip factor.
Just in the process of building a HT with plus tyres to get a feel for it, and if it works my next bike will be something like a Flare Max or Ibis something max.
Around Cannock the fatty was hilarious and I found myself trying (and succeeding in most instances) to get up stupid hills that the normal FS wouldn’t get purchase from regular 2.25 tyres.
Going down I’m not sure about yet, but basically with your budget I’d at least try throw a leg over a plus to see if it’s your thing.