I haven’t read an awful lot of general histories of Finland, but this is one which I liked. It is, “From Grand Duchy to Modern State: A Political History of Finland Since 1809” by Jussila Osmo. It is good read and written by a native rather than an outsider. It has a distinctly nationalist bias but it does not colour the narrative too much. As the title implies it deals with with the political history of Finland, so if your looking for social history or cultural history this book will generally disappoint. It covers history from 1809 until about the year 2000 so if your looking for very contemporary information I would suggest the good old interweb.
Cheers and I hope you Lapp it up.