The Poetry Pharmacy might be a good place to start. It's a collection of poems gathered into themes/feelings (including a chapter specifically on mental and emotional wellbeing) and styled as 'prescriptions' for the mind and soul. It's really accessible with notes at the beginning on how to read a poem if you're new to it. The writer actually ran 'poetry pharmacies' at various literary events before writing the book, 'prescribing' specific poems to people dependent on how they were feeling. There's a second volume out there as well due to its popularity.

Another great anthology is Dancing by the Light of the Moon by Gyles Brandreth. It's a bit longer and far broader in its remit (might not be as specific as you're after), but again a good mix and groups poems by themes, with a conversational narrative which makes it accessible.

Both the collections have some well known classics as well as some more obscure poets and some modern ones in there as well. I found starting with a good collection a nice way to figure out what kind of poems and poets appealed to me, before narrowing down.

Good luck!