By selecting K1, you at least know you should get a King Bed in the room. The other options depend on hat is available and could be two single beds, two double beds etc, depending on the specific hotel. I always select the bed type if I want something specific.
Here's what I did in a similar situation at a Hilton recently.
2xDouble beds was quite a bit cheaper than a king bed. Don't really care what I end up when travelling by myself, but of course prefer a King.
Booked the double room, but put a note in to say something like I'm happy with the double, but don't require 2 seperate beds so happy with either that or a another room if it's easier for the hotel.
The Hotel applied my HH Gold to the booking which has a preferred King Bed. So I ended up in an Upgraded King Room.
Saved quite a few $ with that, but would have been happy with the double if given.
So if same price, go for what you want. If cheaper for room chosen at check-in, then go for that if you are happy with a double bed room on the 2nd level facing the laundromat. Although a King could quite easily be in the same location or you could be upgraded to a room that actually matches your profile with HHonors.
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When travelling in the USA I always book a king bed room but on a rate that can be cancelled without penalty.i then check on the net a few days before arrival.If all room types are still available I will usually swap to the room selected at checkin if it is significantly cheaper and only once did not get my king bed.Unfortunately on one occasion a large group booked to arrive the day before me,the place was full obviously and single beds it was.