I'm not sure, but it seems that you may not be aware that "amd64" (aka "x86_64") is the name for 64 bit x86 CPU architecture. Modern Intel and AMD CPUs both support "amd64" CPU architecture (whilst still supporting the older "i386" aka "x86" standard too). The reason why it's named "amd64" is because AMD created it after Intel had already created "Itanium 64" (aka "IA-64"). The advantage of "amd64" is that it can support both "legacy" 32 bit operating systems, as well as 64 bit operating systems (IA64 required a specific 64 bit OS). After the success of "amd64" Intel did a U turn and followed AMD's lead and adopted their tech. But by that stage AMD had already named it.

It is perhaps also worth noting that TurnKey has only provided "amd64" builds for the last ~10 years. So if you've ever had a TurnKey guest on this particular machine, then it definitely supports "amd64". I also did a quick google and whilst the Dell you refer to is quite an old machine (from what I gather) I'd be surprised if it didn't support 64 bit. If you have the CPU model number, you can look it up on the Intel website and that will explicitly tell you. Please feel free to post back with more info if you need some guidance or input there.

So given the above, I'm almost certain that you would be able to install from the deb that they supply. Having said that, Docker might still be an option if you're interested in the learning curve and having a play with it.

Whilst it's an interesting technology and I do see the appeal, personally I'm not a massive fan. Lots of people are though, so they must be doing something right. To explicitly respond to your question, no we do not have a Docker appliance (with or without Portainer). We do have hopes to develop one but not sure if we'd use Portainer as the front end or not. I'll take your post as a vote for that! :)

So if you did still want to try Docker, you'll need to install it yourself. Core is as good a base OS option for that as any IMO.