Welcome to the forum Dave.
More knowledgeable people will follow on, but I'll start with the part of which I am sure.
The fiancee and the spouse visa are both settlement visas.
The fiancee visa is only a 6 month duration, and you must get married within that 6 months. Before the 6 months is finished you will need to apply for Further Leave to Remain (FLR) which will involve paying a large fee again. The FLR is of 2 years duration.
The spouse visa has a validity of 2 years (plus 3 months from date of issue).
After 2 years in the UK you can then apply for Indefinite Leave to Remain (ILR). So from this, you can gather it is less expensive in the long run, if you go for the spouse visa.
I would think the Unmarried partner visa has the same duration as the spouse visa, and you have other options like ILE, which I'll leave for others with more knowledge to answer.
Hope this helps in some small way.