How could your living space be so small that you're not able to fit a desktop in there somewhere? I mean, I'm on a 55 inch desk with a larger mid-tower, two monitors, and mic/boom arm + peripherals and it all fits on it fine. And my room is basically a guest room in size, so not really meant to have someone living in it all the time. You could always opt for a smaller desk, and put the tower on the floor with a piece of wood or cardboard underneath it, then you'd likely have enough room for a monitor and peripherals. There's so much more value in a PC, especially for rendering/3D modeling/etc. Cooling being the biggest reason. But I get it, space constraints are a PITA.
Laptops have to not only cool a CPU, but a GPU, all in the size of something no thicker than most keyboards. This only becomes more noticeable as the components get more powerful and more power hungry. When you're doing something as intensive as rendering for a fair bit of time, the machine is likely going to throttle and slow down renders tremendously. I'm aware that laptops are built for high heat, but that doesn't mean constantly throttling at high heats is good for the component itself. So, that said, if you're insistent on a laptop, cooling should absolutely be a priority. It should be the priority. Do your research on mobile GPU (obvious, but you should be looking at Nvidia GPUs) skews and have a solid understanding on each one and their performance differences. RAM and CPU, respectively, should come after. RAM, in this case, is probably more important than CPU - unless you'd rather go the CPU route for render. In which case, you'd probably want to look for the highest-end CPU you can get in your budget. You're probably looking at anywhere from $1,800 to $2,500 for a laptop good enough to render at decent speeds. If not more. It'd be hard to recommend anything without knowing your budget, though.
The problem there, again, is that for that budget, you could build a PC that would absolutely curbstomp it in every practical/realistic way. Even in a small form factor case.
