Okay, for starters, The Kenmore machine (Im guessing thats the one in the centre?) looks to be a similar sort of machine to the lower-end Sunbeam Espresso machines (say em3600, the portafilter innards look almost exactly identical) its possible that your grinder is not set fine enough grind for the machine.
The soupyness of the puck after extraction is a side effect of the Pressurised "crema system" baskets. Letting the portafilter sit for a minute or two usually lets the soupyness drain away, though its annoying if youre doing multiple shots
Also, You may find it difficult to get a good pour with the single basket, Most folks seem to just put them in the third drawer down and forget about em.
Best mod for these machines though, is changing the basket for the Breville or Krupps unpressurised basket, but that might mean a bit more of an outlay for a better grinder if your current is not capable of fine enough