For regular desktop use (and graphically lightweight games) you don’t need a dedicated GPU (assuming your CPU has something built-in).

If you want to play games with heavier graphics than you need a dedicated GPU.

Generally speaking: AMD GPUs are preferred, since Nvidia GPUs are harder to get working due to extra drivers. Though I’ve heard it’s definitely possible.

Edit: second hand is usually fine, but watch out for stuff that’s been used for cryptocurrency mining; those have been worn down a lot more.

If you only do regular desktop stuff or just some light gaming, you will probably be fine with integrated GPU. But beware, your CPU does need to have one (not all ones do). Also, when you are using an integrated GPU you are dedicating part of your RAM for that GPU so in the end you will have less RAM available, usually it is something like 2 GB, but it is something to keep in mind.

To be honest, I would probably avoid latest GPU stuff, most of them are not worth it in my opinion. Too expensive and too power hungry. But it depends on your options and what you want to play.

Second hand is usually fine. Even if it was used for crypto, if it was properly cooled and taken care for (although that is usually hard to know for sure).

You will have the easiest time with AMD GPUs, they are basically plug and play. The only reason for going with nvidia would be their proprietary stuff like DLSS and better ray tracing. Or if you do some work that could benefit from CUDA (machine learning, 3d modeling).

To be honest, it doesnt matter if its about a linux distro or windows, to answer your questions.

You need a dedicated GPU, if you have tasks, that requiere one. And this depends, how powerfull is your iGPU. There is actually nothing special about iGPU, despite missing dedicates vram. You can easily compare their performance an decide.

Do I need a dedicated graphics card? I'd like to run an HD display as a minimum. (I don't have a 4k monitor at but I wouldn't mind upgrading later if I can save up for one.) Mostly, I'll be streaming or playing videos.

More important about this is to use hardware accelerarion if watching videos. vdpau or vaapi are recommended. Check this out here.

I wouldn't mind playing some games but is a dedicated GPU needed?

What is your actual gpu? There is no general answer.

If I should look into a GPU (I can always add it in later), what should I look for? (I'm not really interested in the latest AAA games). I wouldn't mind playing HOI4 or Victoria 3 as I hear so much about them.

It depends what you are trying to do. Look at the minimum system requierements of the game you want and than buy. Look here for HOI4.

I prefer AMD GPUs on Linux, because the drivers from NVIDIA are not that great. I use a AMD RX580. Its few years old, but enough to play most games prior to 2021 on 1080p with high settings. My Notebook has a RX Vega 10 iGPU, which is very usefull.

What are your thoughts on second-hand GPUs? This will obviously cut costs but is there anything to watch out for?

I would not buy a GPU which was used in mining rig. Those GPUs worked full time on heavy load and have probably a lower life span.

Edit: Typo

If you're not playing AAA games, i'd recommend you getting an AMD APU. It's a processor with integrated graphics, i use Ryzen 7 5700G (it's under $200). Works perfectly on Linux and should be able to run the grand strategy games easily, for reference i can play honkai star rail at decent framerates (in some zones) 1080p.

I started my budget computer with a Ryzen 3 3200G which i bought used from Aliexpress, upgraded to 5700G last summer and maybe this summer i get an intel arc gpu but honestly i don't need it it would be just a quality of life increase. Currently i have no use for the 3200G but i plan to repurpose it into a home server with a mini atx motherboard.

Go for AMD GPU. There's a reason people advise against using Nvidia for Linux.

https://community.kde.org/Plasma/Wayland_Showstoppers

There's a section for Nvidia alone in the above page for example.