It’s Pokemon Bank (transfers pokemon Gen 5 and up) that will be at its end of service, and will no longer be compatible with Pokémon Home.
At minimum, you would need a GBA-compatible DS (for GBA to DS), a 3DS (for Gen 5 and up), a single switch and a Home subscription to get everything into home.
You also at least need a Gen 4 (I see you have HG) game and BW2 in its Post Game to transfer beyond the DS era.
If you have some games already, great.
If you can get a couple more in a fast time, also great.
Just to correct some information:
It’s Pokemon Bank (transfers pokemon Gen 5 and up) that will be at its end of service, and will no longer be compatible with Pokémon Home.
At minimum, you would need a GBA-compatible DS (for GBA to DS), a 3DS (for Gen 5 and up), a single switch and a Home subscription to get everything into home.
You also at least need a Gen 4 (I see you have HG) game and BW2 in its Post Game to transfer beyond the DS era.
If you have some games already, great. If you can get a couple more in a fast time, also great.