I've never seen the coop in person and in general not a fan of most prefab coops. That being said, from the photos (for what that's worth), it appears to be of decent enough quality. OSB interior with t1-11 exterior. The frame timber looks to be untreated so I have a few suggestions that take a little effort, but generally no "handy man" knowledge.
First I would at least prime the exposed OSB. It wouldn't hurt to paint it and you can take a photo of the coop to Lowes and they'll color match if that's important to you.
I would also paint the coop floor with some sort of weatherproof paint. Blackjack 20 can also be found inexpensively at Lowes. This is a roof covering that is sort of like a paint on version of "Flex Seal" (from the TV infomercials). I don't know what kind of bedding you're planning, but this should protect the floor from moisture and such from the chicken's waste and such. You could probably get away with using flex seal actually, with such a small footprint - this gives you some color options (but it's also paintable to match the coop if you wanted) and is applied via aerosol can vs a paintbrush. You could probably even just paint the floor if you didn't want to bother with the weatherproof stuff...
Painting the untreated timbers probably isn't possible because the wire seems to be attached with fencing staples that would be a pain to remove, and at that stage you'd almost be building the coop. Good news is that it really isn't necessary so no loss. I would also not paint the roost and the interior frame timbers also probably don't need painted. Tape them off if you don't want any paint to get on them when painting the OSB (if you choose to do so)
Sidekick and Hero appear to be basically constructed the same. If you can afford to buy the larger version up front it would allow you an extra hen or two, or give your planned flock a little extra room if you don't want the extra bodies in there.