Advice on hardware/software setup

I am looking to get into self hosting, for setting up a simple plex + nextcloud server. However I also would like to buy a nice desktop pc soon which I would like to access at at least two locations, I think I should be able to combine this with a home server but I unsure what the best way to do this/what are the right software tools for this. The situation currently is: I have a television in my living room on which me and my partner regularly game (for now using an hdmi cable and a shitty laptop) and we have a study room where we work and play games involving a keyboard (currently also on laptop). I would like to be able to access the compute of the desktop in both locations, for this I see two options:

1. Setup a small mini pc that is also connected to the tv, use it to always run nextcloud + plex, set the main pc in the study and use steam link to forward just games to the tv.
2. Put the pc in the living room connected to the tv and use it as a home server, and setup a small pc in the study connected to the monitors and other peripherals. Then connect to the main pc with a different tool.

Option 1 seems more simple but a bit limited, while option 2 should give a more powerful home server but also increase power draw (I have been thinking if there could be a good solution to this using wake-on-lan when it is not in use) but also needing a more refined way of connecting the two pcs. For sharing the computational power I have found steamlink, a remote desktop (like anydesk/teamviewer), and I have some experience with using SSH which is nice for coding but doesn’t seem to work well for anything graphical. Any advice or insight what would be a good way to set this up would be appreciated!