Hi Marieke,

You might be able to get by with a roomy two-person tent for two plus a compact [half] dog, so don't limit yourself to strictly three-person models, because there are far fewer of those to choose from.

Something like the Big Agnes Copper Spur HV3 Expeidtion fits your criteria other than cost, but might be more than you actually need. They have a two-person model and also a lighter "three-season" version that's cheaper and lighter, but has more mesh in the canopy.

I would recommend a two side-door model over a single door in front for two plus a dog, and as close to free-standing as possible for ease of setup.

Alternate shelters like teepees are an interesting option but not necessarily best for beginners.

Good luck!