If you have the make/model of the all in one unit, it would give some idea of what kind of capability would be a good upgrade.
To give you some idea of a starting point:
I3-10100 is a good gaming processor that includes basic HD630 graphics.
HD630 is about twice the capability of the 710 graphics in the ibuypower offering above.
https://www.newegg.com/intel-core-i3-10100-core-i3-10th-gen/p/N82E16819118165?quicklink=true
The prices of intel processors have been bid up because of the current shortage of discrete graphics cards.
Here is a review of the i3-10100 as a gamer:
Intel's Core i3-10100 is the most affordable Comet Lake "Core" processor. Unlike its predecessor, it finally has HyperThreading, which brings the core configuration to 4c/8t. Our Core i3-10100 review takes a close look at how Intel's new budget offering performs against AMD Ryzen 3 3100 and 3300X.
www.techpowerup.com
A very good long term option is the i5-11400 with HD730 graphics that is about 3x the capability of the GT710.
Here is a review of the I5-11400F.
The Core i5-11400F coupled with a B560 motherboard make for an interesting build configuration, as it's significantly cheaper than the Core i5-11600K/Z590 and less than the cost...
www.techspot.com
I might explain that the F suffix processors do not include onboard graphics and are therefore a bit cheaper.
Minecraft is not a terribly gpu sensitive game so I expect that integrated graphics would
do just fine, at least for starters. It will let you know what, if anything you might want as an upgrade.
Most any lga1200 motherboard will do.
You can find some <$100, but I would go with a B560 based motherboard such as this for $110:
https://www.newegg.com/p/N82E16813119385
Buy 16gb up front in a 2 x 8gb kit.
Perhaps this g.skil 3000 speed for $77:
www.newegg.com
Do not buy a cheap quality psu.
The wattage you need will be determined by the graphics card you eventuallly end up with.
Here is a handy chart:
http://www.realhardtechx.com/index_archivos/Page362.htm
550w can handle a very strong graphics card.
Often 650w costs minimally more.
Here is a seasonic 550w for $ 85 with a 7 year warranty. The 650w is only $90.
www.newegg.com
I have no problem overprovisioning a PSU a bit. Say by 20%.
It will allow for a stronger future graphics card upgrade.
It will run cooler, quieter, and more efficiently in the middle third of it's range.
A PSU will only use the wattage demanded of it, regardless of it's max capability.
You will need a case, most will do.
Fractal design are not expensive, $55 or so:
https://www.newegg.com/black-fractal-design-focus-g-mini-micro-atx-mid-tower/p/N82E16811352068
They come in other colors. The kinked case is a smaller MATX size which matches the motherboard i linked above. Matx has 4 expansion slots, ATX will have 7.
I imagine you can reuse your monitor, keyboard and mouse.
Do not worry about assembling a pc. There are videos about it.
Parts are keyed to fit only one way so you can't go wrong if you do not force anything.
Read the case and motherboard manuals, cover to cover, before you start.
These forums are very helpful if you encounter problems.
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