Should I buy a desktop or laptop for working at home?

I will prefer a laptop because is potable

Having had both, I'd for with a laptop.  They're smaller, just as powerful, and you can take it with you on trips.

It's a preference thing and also could be dependent on your home situation, space, lack of space etc.,, if its's a big screen then yes go for a desktop. If you want to be able to move around then laptop for sure. 

I'd let your work supply the PC, if you are self employed it depends on what your work is.

You are a bit vague on the information. Is WFH a covid thing that's temporary? will you be travelling? go you need the greater potential cpu/gpu a desktop can provide? Please give more context.

I have a laptop but my working experience improved a lot when I added a nice big monitor for more screen area and better reading. I like the flexibility of a laptop but to be honest it stays plugged in for weeks at a time.

I work at home with a laptop and a second monitor. The laptop was only $650 and using logmein I do 3d solid modeling using the computational power of my work PC. I prefer the convenience of being able to move the laptop around when I am not doing work.

To have a fully productive workstation you need a couple of monitors and a real keyboard and mouse.   You can hook up a laptop that way, but it may cost more to get something powerful enough.    Personally I find having both a desktop and a laptop to be the best, but it really depends on the type of work you do and how much money you are willing to put into it.  

Both Desktop and Laptops have their own perks. Moreover, going for a laptop or a desktop really depends upon your work. I prefer to have laptops because if I want to move from one place to another place then still I can use it for my daily work.

You should buy Desktop at home.

It depends on the sort of work you do at home.

For my normal day-job, my employer provides an HP laptop. I added three external monitors and desk-mount arms, a docking station, external keyboard and wireless mouse. Lots of emails, video conferences, MS Word, PowerPoint and Excel work.

I do video (capture and editing) as a hobby. I use an Apple iMac 27" and use a spare video input on a couple of the monitors for additional monitor space for FinalCut Pro and Logic Pro.

We don't know what sort of work you plan to do from home, which applications you are expected to use or your level of skill in order to be your own "tech support".