Cases/PSUs for a slim factor HTPC?
I've been thinking about building a slim factor HTPC, similar in size to an Intel NUC. I would like it to be the cheapest possible, the usage would be for streaming, both paid services (maybe game streaming services like Geforce Now, Steam Link or Shadow) and local files via Plex and to use Kodi as interface. The idea is to have something that is able to run the current formats like 4k HDR and Dolby Atmos but just using the integrated graphics card.
I've seen that there are cases that match my requirements but I'm a bit confused about the PSU needed for that. I've seen there are cases with an integrated PSU but they don't seem to provide enough power for a full PC. Then there are other ones that can be plugged to external PSUs but in this case it seems like most of the budget would go in the case and the power supply.
I was thinking on using either an i3 or a ryzen 3 for my build and then a cheap motherboard with 4/8gb of RAM and a small SSD/M.2 drive.
Has anyone built a similar system or can anyone point me in the right direction about what cases/PSUs would be a good fit for this kind of build?
P.D.: I've seen cases from Streacom which seem nice and would probably do the work but they alone with the PSU cost almost $200.