In Amethyst, settings > relays, there are a couple of recommendations for Search and DMs. But if you go to the General Relay section and tap "Default", you can use some of those for your public/private inbox, public outbox, etc... Some that are really good, that can be used for DM, private/public inbox/outbox that have come up in discussions (I don't remember where) have been:
wss://nostr.mom 
wss://nos.lol
wss://relay.0xchat.com
wss://nostr.bitcoiner.social
The others in your General defaults list are probably really good options as well. These will definitely get you in the mainstream, from my experience. Others may want to chime in here...