Planning build: Power efficient headless steam machine, and later upgrade for AI tasks

Background

I'm planning on building a secondary server that can process more intense tasks than my current basic home server. Tasks such as light gaming (think "remote Steam Deck"), and later allowed to be upgraded with a Nvidia graphics card to handle AI tasks, such as LLM and SD.

The problem

While I have no problem picking parts to build this as a "desktop computer", I'm completely lost when trying to make it power efficient for idle load (if it's even possible with a power-hungry Nvidia card). I'd appreciate some guidance even if it's not a full parts list suggestion!

Watching Wolfgang's videos has unfortunately not translated knowledge into practice for me yet. At least I know TDP isn't an absolute determining factor anymore.

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Planning the build

Due to a limited budget, the idea is split the build in 2 phases.

Phase 1 (gaming):

• Budget: $1000 (ideally below ~$800):
• Use for local headless gaming (with bazzite?)
• At least as powerful as a Steam Deck
• Parts:
  • APU:
    • Perhaps: "AMD Ryzen 7 7800X3D ($400)"
    • or "AMD Ryzen 5 7600X ($300)"?
  • Motherboard:
    • No specific requirement, will mainly just use the PCIe x16 slot for a single GPU when upgrading in "phase 2".
    • Okay with gigabit ethernet and basic I/O.
  • Power supply:
    • Power efficient power supply that can handle a class 4080/4090 card.
  • Cooling:
    • Air-cooled preferred
  • Storage:
    • Samsung 990 PRO NVMe M.2 SSD 1TB (~$100)
  • RAM:
    • Corsair Vengeance LPX Black DDR4 3200MHz 2x16GB (~$70)
  • Case:
    • As long as it fits a large graphics card

Phase 2 (AI: LLM/SD):

• Budget: ~$2000
• After 1-2 years, upgrade with Nvidia graphics card.
  • Ideally something with 24GB VRAM, like the 4090.
  • Prefer Nvidia due to compatibility with SD.
• Open for suggestion, since wanting a low power draw with a 4090 might sound contradictory.

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In case I missed any crucial information, let me know!