I have setup and run what are basically HTPC’s for decades now. Kodi running on a Debian based Linux distribution or just Debian is a solid recommendation and has lots of support for infrared remotes, but kodi can be very fiddly to setup properly. It will work, but don’t expect it to work “out of the box”. You’ll probably still need a mouse and keyboard for anything outside Kodi. You’ll have to read a bunch of documentation and do some customizing to get the most out of Kodi. It’s still easier than most other setups, but it will feel very frustrating if it’s your introduction to Linux too.
I’ve moved to using my HTPC primarily as a server. Once you get comfortable with linux and docker, setting up new server services like Jellyfish, Plex, and and *ARR stack is relatively trivial. The advantage here being that you can serve your media to any device that can connect to your server. For me that means one library of media to share with any TV in my house, any mobile device I own, and any friends and family computer savvy enough to download the right apps and setup an account. If your network (and your Internet connection) isn’t reliable this kind of setup may not work very well for you at all. For example, Plex account authentication will fail is you don’t have Internet. Jellyfin and Kodi fair better when Internet is only available occasionally or is unreliable.
My least favorite part of using Kodi was setting up the remote. Even worse was trying to configure controllers for retro gaming. The situation is MUCH better than it was, but is still far from easy. I was kind of able to side step the remote problem because now I can just use the remote for the TV (if it supports the Plex or Jellyfin apps) or another streaming stick like fire stick, Nvidia shield, or Roku. My Nvidia shield can pair with any Bluetooth controller and runs RetroArch so that problem was side stepped too. ROMs can be copied via samba shares or loaded directly by a USB drive.
TLDR: Kodi has built-in support for IR, but streaming sticks are cheap, and in the long run I found setting up a server was more versatile, more reliable, and less stressful. I know, I also hate it when people ask for a specific solution and others recommend asking a different question. But in this case, my experience is that IR remotes suck, are flaky, and not worth it if there is any other option.
Yes, I’ve done almost exactly this while traveling. You can even carry around a couple variously configured sd cards for different use cases. I had one with jellyfin for sharing locally and also Kodi for direct HDMI connection to TVs. There is a in app on Android for jellyfin called findroid that allows offline copies from the media server, which allowed me to not need the thing powered the entire time I wanted to watch something on my phone, just long enough to download it. Adding samba shares adds a other layer of accessibility. I had another SD Card with video game ROMs for retro gaming, but this one got left at home because it requires controllers and I didn’t think I’d use it that much. I had another with “little backup box” installed for automatically backing up my photos and videos after a day out exploring with my camera.
I used a Raspberry pi 5 for all of this, running from a battery backup, because I didn’t really need a keyboard once I had remote connections to my phone sorted out. Pick a rugged case and you case just toss it in your bag of chargers. It took up about as much space as a pack of cigarettes. Another option would be the Raspberry Pi 400, built into a keyboard. A little bulkier, but maybe more resilient in the face of technical difficulties.