The ultimate goal in any war must be peace.
Peace through communication and negotiation might be possible. But ignoring the fact that we don't have any track record on how good they are with keeping negotiated contracts... we absolutely know that humans are terrible at this. Humans can't be trusted to keep a contract for 5 years... never mind 500 or 5000 years.
Peace through through complete extermination works. But without knowing the Thargoid source we have no idea if extermination is possible.
Peace through leaving them alone worked for the last million years. I don't know how to control humans to leave them alone though. Maybe move colonies away from Thargoid space and have governments permit lock the restricted areas? Long term (100s or 1000s of years) this won't last. And Thargoids live on big time scale.
Long term the big problem lies with humans. Not Thargoids.