Tiered cake help

Dowels or straws on the bottom tier will really help the structural integrity of your cake, and take away any worry about the top tier adding too much weight. Don't worry too much about anyone eating them; they'll be big pieces and really easy to spot, plus you can remove them when you serve the cake. A six-inch cardboard round under your top tier is important too, it will give a sturdy platform for your dowels or straws to support. You can also run a dowel through the middle of both tiers to really guarantee the top tier stays in place during transport. I use a dowel that is roughly the same diameter as a pencil and the same height as my stacked cake, put it in an electric pencil sharpener so one end is sharp, and push it through. It should go through the cardboard base under the top tier super easily. Just make sure your cake is well-chilled when you stack it, dowel it, and transport it and you'll be all set.

I don't think you need dowels unless you heavily fill the layers with icing.

I usually cut rounds out of foam core, but a premade cardboard cake round is a good option. You definitely want something to rest on the straws, or there's no point to the straws.

I like your second option: the 6" tier on a cake board. I made similar cakes when my daughters were small. I know people use straws as hla suggests, however, when I asked semi-professional baker in my daughter's school about this, her advice was that one should never use things within the cake that can possibly get sliced by the knife and become a choking hazard when served. A butter cake (I always used Anna's Swedish Butter Cake from A Piece of Cake by Susan Purdy) should be able to support the layers.

I like to use drinking straws as internal support instead of dowels (per Rose Levy Beranbaum). Put the first one in the center, then mark where you need to cut it. Pull it out and cut the other straws to the same length. For a 6-inch cake you want a central straw, plus 6 around the perimeter. I've done this with butter cakes dozens of times. The yellow cake recipe I most commonly use is the one in The Cake Bible by RLB. The Smitten Kitchen one sounds really good, and I suspect it will work well.