For a powerful entry level PC, I am recommending the i3–10100 quad core right now at $121. You can get an inexpensive Socket 1200 B460 full ATX motherboard for $99.
The ASRock B460 Pro4 is very adequate for a basic budget motherboard. The muted gray decor should not clash with a pink case.
The Apevia Enzo hits Amazon shelves Feb 4 2021, and will initially cost $59. Complete the core of this PC with 16GB of DDR4 3200 (white to avoid color clashing)
A 1TB Crucial P2 NVMe SSD is selling for $92 right now on Newegg and should give you years of extremely fast storage with no need of an upgrade. The crucial P2 is a rather ugly blue, but you should be able to hide it under the M.2 heat plate included with the motherboard. What I love about building with a M.2 drive is that you have zero cables to clutter your nice new build—other than the necessary ATX power cables. If you want to add another drive later, you have a spare M.2 socket (so, still no cables to deal with.)
I’d probably power this with a Bronze rated EVGA 450 BR power supply for $50. Its black cable harness makes it easy to hide in a black case.
I’m hard pressed to recommend a graphics card at the moment as prices are outrageous. Unless you want to pay $300 for a GTX 1650 that retails for $159, I’d suggest getting a used RX 570 on ebay for $120 or so.
With a used RX 570 graphics card this build should come in at about $620. If you want a used RTX 2060 with hardware ray-tracing support, look at spending close to $950. A third option is to build the PC without a graphics card and use the integrated graphics for a while. This will drop your initial cost to $495 or so, and still be able to play Overwatch and Minecraft at very low settings.
In Summary this is what you need
Motherboard, CPU, RAM, SSD
Graphics Card (optional)
Case and Power Supply
Just so you are not scared to go without a graphics card for a few months while the GPU-supply chaos subsides, this is Overwatch at 720p on low settings. It did not drop below 40fps even once. Minecraft is almost entirely CPU dependent, so you will have everything you need for that except ray-tracing support. Likewise, GenshinImpact will play at 45fps at 720p on low settings with integrated graphics.