You can become a lawyer with any degree, and not all law degree graduates secure a training contract or pupillage on graduating (in fact, outcomes are rather poor in that respect).
You need a BPS accredited psychology degree to become a professional psychologist of any variety, however you don't seem interested in those career areas.
Note you can become a primary (or secondary) school teacher with any degree as far as I'm aware once you complete your PGCE and QTS? For secondary teaching your degree field will inform what subject(s) you teach although that is not necessarily the case for primary teaching I believe.
You can go into any of the same kinds of graduate roles with a classics degree as any degree holder can e.g. the civil service, the media, law, investment banking and management consulting, accountancy, and any of the general corporate based grad schemes as well.
Ultimately your degree is not what determines your career prospects unless you're aiming for a specialist field requiring a particular qualification for professional registration (e.g. psychologist roles). What determines your career prospects is what you do to make yourself employable by pursuing internship and work experience opportunities, developing relevant transferable skills by taking on leadership/committee roles in societies etc, and preparing for the battery of psychometric tests and assessment centre exercises and interviews you need to pass through to get a graduate role in the first place. None of that changes based on what degree subject you do, and for most employers and roles the degree itself is merely a tick box - does the applicant have a 2:1 or higher degree in any subject Y/N? If Y move to next stage of application. And beyond your first job your degree becomes largely irrelevant (unless again, you are in some specialist field like psychology, healthcare roles, etc).
Pick something you actually have an intellectual interest in for your degree, because it'll make grinding through the rest of the stuff you'd have to do on any degree to make sure you can land a job at least marginally less painful because you'll have something to look forward to (i.e. your lectures and the actual content of your degree).