When working with exterior wood, I use 1/2 linseed oil 1/2 mineral spirits. The spirits help the oil absorb deeply and then they evaporate and just leave the oil. Wipe away any residue, although I find that virgin wood rarely has residue left over - it all absorbs. Use a disposable paint brush and work over the dirt or grass - the oil will stain concrete/asphalt (don't ask me how I know this -- my DH isn't happy about this). I've been using this mixture for my teak patio furniture for the last 10+ years and am happy with the results.
I went with a natural look for the T1-11 on the exterior of my coop, but I like the protection of paint. Use oil based Kilz and exterior paint, even on the interior of the coop. It will adhere better and withstand the fluxuations of temperature much better than an interior paint will. PS - if you're willing to spend the time/money, I recommend painting your interior. It might seem like a hassle now, but trust me, the first time you have to clean out your coop you're going to be REALLY glad you did it. And after a long winter of being locked inside, your coop is going to be DIRTY. Do the floor while you're at it.
Also, consider hardwiring your electrical service. You are going to need it and having it hard wired looks better and is so much safer. You'll need power for keeping water thawed and providing heat/light should you choose to do so.
PS - that playhouse is amazing. I have 3 daughters who would DIE to have that in their backyard. My chickens are spoiled...
Feel free to PM me anytime if I can be of assistance.
cc