...I have many questions.
Honestly, it might just be better if you just provide a budget, name the country you're looking to purchase from (maybe including a link to your usual retailer of PC parts), and I'll see what I can do.
Alternatively maybe take a look at http://PCPartPicker.com and see if they have a local version for your country (click the country drop-down menu in the top-right of their website).
Anyway, CPU-wise, Dolphin only really cares about having 2 fast CPU threads. That being said, the Athlon 3000G uses a Zen1 architecture which Dolphin was, for whatever reason, one of its worst-case scenarios. Therefore, in terms of just raw CPU performance, the Intel build would be faster.
The bigger problem however is that the Pentium you mentioned is an Alder Lake-based part that uses an LGA1700 socket, and the Intel motherboard you listed uses the LGA1200 socket (which is what the i3-10100 uses).
That being said, honestly, Alder Lake's single-threaded performance, while very fast, is probably actually overkill for Dolphin.
Another issue is that, if you're using integrated graphics (and it looks like you are), then using only a single stick of RAM will substantially hamper your integrated GPU's performance. Yes you're only doing 720p to 1080p but, still... it just seems like such a small thing to cheap out on since 2x4GB of RAM is pretty darned cheap nowadays comparatively and, honestly, unless you wanted to use Linux or an older version of Windows (e.g. Windows 7), using only 4GB of RAM could be touch-and-go.
While I'm here, may I ask if the Pentium G3258 is something you'd be interested in? It goes for like $15 on ebay and, in Dolphin, should be just as if not faster than the Athlon 3000G at stock speeds in terms of just CPU performance. Thing is though, the G3258 has an unlocked multiplier and will easily overclock to at 4+GHz with not that much heat output (it's only a dual core after all!), many hitting 4.2GHz and even 4.5+GHz not being uncommon, while the Athlon 3000G tends to max out at a hard 4.0GHz.
The real issue is that the G3258 needs DDR3 RAM, an LGA1150 motherboard, and its iGPU isn't great for higher resolutions though is fine for 480p (especially with dual-channel RAM paired with Linux). Of course, it being so cheap means that you could get a used discrete GPU as well - even the old HD4670 for like $20 runs circles around it. Also, for these sorts of older hardware, you may need to use Linux in order to get proper driver support (and, if you do go the Linux route, then you'll tend to have an easier time if you stick with AMD or Intel graphics) But even then, the Linux drivers for AMD and especially Intel tend to be superior compared to their Windows drivers.
Speaking of Linux, protip: using the official Nintendo 1st party GameCube USB adapter with Dolphin is much easier on Linux than it is on Windows:
Another issue is that, unless you specifically went with a more-expensive Z97 motherboard, then compatibility with the G3258 and/or the ability to overclock it can be hit-and-miss unless you can find reports from other people that mention their specific motherboard that they overclocked a G3258 on. Also be wary of 81/87-series motherboards as they may be "compatible" only after a BIOS update which itself can usually only be done if you had a CPU that was compatible without the BIOS update unless the motherboard specifically supports USB flashback or the like (the ability to update the BIOS with nothing but a power supply and a USB drive formatted to FAT32 with an MBR partition table).
Honestly, it might just be better if you just provide a budget, name the country you're looking to purchase from (maybe including a link to your usual retailer of PC parts), and I'll see what I can do.
Alternatively maybe take a look at http://PCPartPicker.com and see if they have a local version for your country (click the country drop-down menu in the top-right of their website).
Anyway, CPU-wise, Dolphin only really cares about having 2 fast CPU threads. That being said, the Athlon 3000G uses a Zen1 architecture which Dolphin was, for whatever reason, one of its worst-case scenarios. Therefore, in terms of just raw CPU performance, the Intel build would be faster.
The bigger problem however is that the Pentium you mentioned is an Alder Lake-based part that uses an LGA1700 socket, and the Intel motherboard you listed uses the LGA1200 socket (which is what the i3-10100 uses).
That being said, honestly, Alder Lake's single-threaded performance, while very fast, is probably actually overkill for Dolphin.
Another issue is that, if you're using integrated graphics (and it looks like you are), then using only a single stick of RAM will substantially hamper your integrated GPU's performance. Yes you're only doing 720p to 1080p but, still... it just seems like such a small thing to cheap out on since 2x4GB of RAM is pretty darned cheap nowadays comparatively and, honestly, unless you wanted to use Linux or an older version of Windows (e.g. Windows 7), using only 4GB of RAM could be touch-and-go.
While I'm here, may I ask if the Pentium G3258 is something you'd be interested in? It goes for like $15 on ebay and, in Dolphin, should be just as if not faster than the Athlon 3000G at stock speeds in terms of just CPU performance. Thing is though, the G3258 has an unlocked multiplier and will easily overclock to at 4+GHz with not that much heat output (it's only a dual core after all!), many hitting 4.2GHz and even 4.5+GHz not being uncommon, while the Athlon 3000G tends to max out at a hard 4.0GHz.
The real issue is that the G3258 needs DDR3 RAM, an LGA1150 motherboard, and its iGPU isn't great for higher resolutions though is fine for 480p (especially with dual-channel RAM paired with Linux). Of course, it being so cheap means that you could get a used discrete GPU as well - even the old HD4670 for like $20 runs circles around it. Also, for these sorts of older hardware, you may need to use Linux in order to get proper driver support (and, if you do go the Linux route, then you'll tend to have an easier time if you stick with AMD or Intel graphics) But even then, the Linux drivers for AMD and especially Intel tend to be superior compared to their Windows drivers.
Speaking of Linux, protip: using the official Nintendo 1st party GameCube USB adapter with Dolphin is much easier on Linux than it is on Windows:
Another issue is that, unless you specifically went with a more-expensive Z97 motherboard, then compatibility with the G3258 and/or the ability to overclock it can be hit-and-miss unless you can find reports from other people that mention their specific motherboard that they overclocked a G3258 on. Also be wary of 81/87-series motherboards as they may be "compatible" only after a BIOS update which itself can usually only be done if you had a CPU that was compatible without the BIOS update unless the motherboard specifically supports USB flashback or the like (the ability to update the BIOS with nothing but a power supply and a USB drive formatted to FAT32 with an MBR partition table).
Dolphin 5.0 CPU benchmark
CPU: Pentium G3258 @ 4.5GHz 1.24v
GPU: Intel integrated
RAM: 4x4GB Corsair Vengence @ DDR3-1600
OS: Linux Mint of some variety + [VM] Win7 SP1 x64
CPU: Pentium G3258 @ 4.5GHz 1.24v
GPU: Intel integrated
RAM: 4x4GB Corsair Vengence @ DDR3-1600
OS: Linux Mint of some variety + [VM] Win7 SP1 x64