I did a BA and MA in Linguistics. I loved it because it's so interdisciplinary. I wrote one dissertation about the interactions between music and speech stress in chant, and one about language policy in education where children speak one language exclusively at home and then go to school and learn in another. We could do elective modules on evolutionary stuff, computational stuff, child language acquisition, Old English, semantics and pragmatics (where we learnt formal logical notation), local sociolinguistics... There's a lot of variety.
I'd say aiming at transferable skills is the best way forward, but to look for them in unexpected places. For example, we studied Optimality Theory, which looks at constraint hierarchies to achieve phonological (and others - we just used it in phonology) outcomes - I now use the same principles I learned to order conditional formatting rules in Excel, which I wouldn't have anticipated! We also did a great module where we had a native speaker from a very little-studied language community and we got to help create the description of the language. That was amazing.
Relatedly, moving towards computational linguistics and programming languages can be useful, especially nowadays.
A lot of my fellow graduates have gone into teaching (secondary English or primary), or SaLT. I work in information management.
Having a second language is always useful just because English grammar isn't taught very well beyond basic parts of speech type stuff - means a bit less catching up about cases and such like.
That's all I can think of for now but I may be back!