I have a HP laptop with AMD Ryzen 5 5500u (integrated Radeon Graphics, it should be Vega 7). I was going to download Bazzite to test on my hardware. But I am confused to choose one of them:
I think choosing either option will result in the same link (bazzite:stable). It probably also doesnt matter as much with AMD GPUs as the drivers are part of the mainline Linux kernel and so should just work out of the box with any Linux 
The old/new gpu categories here seems to be mainly for NVIDIA (one would give the user bazzite-nvidia-open, the other would result in bazzite-nvidia).
Hope it works out well, and dont worry - in case you need to adjust the version later (e.g. with/without gaming mode) you can always rebase, the command to do that is right there below the “download” button and the process takes just a few minutes. Enjoy!