If you want to be an archaeologist then it really makes the most sense to study it as part of your degree. I study joint Archaeology and Ancient History and I can't fathom studying one without the other; I believe you need the historical knowledge to interpret the significance of finds during excavation, and you need a sufficient understanding of archaeological practice to evaluate the evidence for "history". Personally I trust archaeology more than texts but I think you need both!
If you are sure you don't want to take it as part of your undergraduate degree then I would suggest taking those modules where possible, skills such as writing artefact biographies are very important.
I don't know about the recruitment processes of any particular companies but put it this way; my supervisor for the last dig I attended (not the site supervisor) didn't have a degree. From what I know experience is far more important that the degree.
I really do recommend having a joint degree rather than a single hons. however, provided you have practical experience then I think a masters degree should bring you up to scratch.
Also, make sure you take a good look at the module choices because there can be a lot of flexibility- within my school of Archaeology, classics and history, I could take any module I please as long as I do my compulsory courses and it fits in with my time table.
experience is key! Not just for the job but so you know that it's the career for you. I only know of one person on my course (out of about 30-40) who still wants to work in the field. If you're sure that you have found the degree course you really want to join then go for it and don't worry about not getting into the field because of it. There will be a way around it.
I hope that made sense, i'm extreamly tired so I hope you could understand my ramblings. Basically if you are sure you want to study a pure history course then do it, I've met plenty of professionals who didn't study it for their undergrad but if you choose to do that gain plenty of experience, take arch modules where possible and maybe look into summer schools to learn the skills you need. Good luck, pm if you want to ask anything- I should make more sense after I've slept!!
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