There are 4 different types of soldering typically used in model making.
Generally we are dealing with brass or nickel silver for our models and for those a solder with a melting point of 145 degrees centigrade is usually used. This needs to be a leaded solder for its flow properties, and this is still available despite the move towards lead free solders in industry.
Many modellers make use of resistance soldering to produce a model requiring minimal cleaning.
For soldering whitemetal parts you need a lower temperature solder such as 70 degree or 100 degree solder and a temperature controlled soldering iron so that the probe temperature can be lowered below the melting point of white metal.
For soldering electrical joints a normal fluxed solder with a high melting point would be used.
Occasionally, for certain tasks such as making crank axles with steel axles, a silver solder would be required.
An article on the chemistry of soldering is useful to explain some of the key points about soldering.