how did you decide upon / find somewhere to live in London?

Got a new job (yay) starting end of January in London (nr Liverpool St). Need to find somewhere to live for myself and my fiancee. Where depends on my fiance finding a job in a hospital somewhere in London, but generally speaking, how does one even start!?

Had a quick look on rightmove this morning. Seems to be no shortage of places, but really I don't know where to start looking.

Also, have no idea about budget. A little bird told me it's a bit expensive to live in London?

Any tips would be great - feeling a bit bewildered to be honest.

Cheers in advance