Love those ITX builds, I have done a number.
On your list, I see two issues:
1. A 200w psu is not going to run anything more than integrated graphics.
And the psu's included with cases are invariably cheap quality. Antec might be an exception.
2. You buy an APU for the decent integrated graphics. When you need more graphics capability for fast action gaming, you will have wasted the price premium on an apu.
More to the point of your objective.
If you are going to use this in a Home theater environment. Start with the case.
I would start with Silverstone which makes a bunch of possible cases.
If you might need a dvd player, here is the ML07:
https://www.newegg.com/black-silverstone-ml07b-mini-itx-media-center-htpc-case/p/N82E16811163256
Another might be the RVZ02b.
https://www.newegg.com/black-silverstone-raven-mini-itx/p/N82E16811163288
Each can handle a full length graphics card.
These cases will require a smaller SFX power supply. 450w wil suffice for all but the strongest of graphics cards.
If you can handle a larger case, ATX power supplies are cheaper.
Whatever you do, DO NOT buy a cheap psu.
Here is a Corsair SFX 450w unit:
https://www.newegg.com/corsair-sf-series-sf450-cp-9020181-na-450w/p/N82E16817139243
For gaming, the graphics card will be the critical component, particularly for fast action gaming.
Something like a GTX1660 super
Here is one for $ 230.
https://www.newegg.com/evga-geforce-gtx-1660-super-06g-p4-1061-kr/p/N82E16814487484?&quicklink=true
One rule of thumb for a balanced gamer is to budget about 2x the cost of the processor for the graphics card.
I happen to like the intel processors for gaming. Their single thread performance is usually higher than ryzen, and that is what games need most.
I have ordered a i5-10100 processor for my son:
https://www.newegg.com/intel-core-i3-10100-core-i3-10th-gen/p/N82E16819118138?&quicklink=true
It has 8 threads and a boost to 4.3
I also ordered this ITX B460 motherboard for $95 It includes wifi:
https://www.newegg.com/p/N82E16813157948?&quicklink=true
Because we will use only integrated graphics(not a gaming system) I ordered a 2 x 8gb DDR4 2666 speed kit.
With a discrete graphics card, ram speed does not matter much for Intel. 2400 or 266 speed is fine.
Budget $65 or so.
I ordered a top of the line samsung 970 evo plus m.2 ssd. But there are other good m.2 devices available
A 500gb intel 660P nvme drive is inexpensive and can hold a fair number of games.
$75
https://www.newegg.com/intel-660p-series-512gb/p/0D9-002V-003Y7?&quicklink=true
Ultimately, all will depend on your choice for the case. Consider that carefully.
In a week or so, I can tell you how it does.