You are right that the first priority is to find an amp that will power your speakers and fill your room with sound - room size is also a factor here - as well as catering for your sources.
I would just consider your current needs plus immediate future needs. Getting an amp for some vague future speaker purchase seems unwise as your tastes and options (finances, where you live, room) may all change, as might the technology.
Do you think you might want to use headphones? Some DACs or integrated amps have headphone outputs.
Both your proposed DACs seem to have volume control. This means you could connect them direct to a power amp. This idea would not be so practical though if you intend to use other sources.
If you really intend to use vinyl then an integrated amp would seem best in that case, making sure that the phono stage in the amp matches the turntable's cartridge [moving magnet (MM) or moving coil (MC)]. I'm no expert on turntables but it seems with the Rega Planar 3 you can choose what cartridge to use. I understand there are phono pre-amps that have a volume control which may mean you can still use a power amp but I don't know enough about the whole vinyl experience to offer advice here.
One thing all your proposed equipment does not have is any form of tone controls or equaliser. Whilst these things were frowned on for a time you may find that what you hear needs some adjusting to get it to your liking. The sound in your room is affected a lot by your room and where you place your speakers and listening position. In addition, recordings are of inconsistent quality, some bass heavy etc.. I think most on here would advice some solution to these issues. Check out this forum on this site:
https://www.audiosciencereview.com/...-acoustics-and-general-speaker-discussions.9/
It's a complicated business so I suggest you just bare this in mind for the moment, consider tone controls when looking at amps, or a small digital equaliser, and see what moving your speakers and listening chair to different positions in the room can do.
On cables, just use what comes with your gear for the moment, or buy cheapish stuff. Most on here agree that expensive cables are a waste of money and even if they make a difference it is tiny compared to positioning/equalisers/DSP or getting better speakers.