I'm curious to know what dogs have to do with the side panel on your case? If you're taking about the dogs fur being clogged up in your chassis vents then you should be looking at cases that have dust filters that you can easily remove and maintain. Fractal chassis's are a good example, as are other brands.
Now, where are you located, how much can you spend on a chassis, what are your current system's specs and what is your preferred site for purchase?
List your specs like so:
I would not worry about dogs slobbering all over the window.
List what is going to go inside.
In particular, the motherboard size, cpu cooler and graphics card.
I have only a few criteria for a good case.
#1 The looks have to appeal to you. You will be looking at it for a long time.
Bust your budget if you need to for a case you love.
#2 The case must hold your parts.
For example, if your motherboard is ATX it is not going to fit in a M-ATX case.
vice - versa will work.
#3 Good ventilation starts with a good supply of fresh intake air to let your cpu and gpu coolers do their job.
I would want at least two 120/140 front intakes. And... I would like an easily washable intake filter.
#4 I am not a fan of aio coolers unless the case has restricted height available for an air cooler.
If the case has 160mm available, you can install the very best of air coolers.