The EEA national does not require any visa or to apply for anything in the UK ( Unless they are from an A2 country and want to work or study in the UK), but for all the others, if they want to, they can apply for a registration certificate on form EEA1.
EEA1 is found here:
http://www.ukba.homeoffice.gov.uk/sitec ... /eea11.pdf
The cost: Free to apply.
For the non-EEA family member ( such as a spouse) there are huge advantages in applying for a residence card on form EEA2.
EEA2 residence card is for when the non-EEA is already in the UK.
The EEA2 residence card is confirmation of the rights that the non-EEA family member has, due to being the family member of an EEA national. They are allowed to work and change employers without the restrictions that can apply with work permits.
It also acts as an entry clearance to allow the non-EEA to more easily enter the UK when travelling with or returning to the EEA national.
This application form can be found here:
http://www.ukba.homeoffice.gov.uk/sitec ... a/eea21.pd
The cost: Free to apply.
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Vaf5 is for EEA Family permits which are for family members who wish to enter the UK - who do not have EEA2 residence cards - and it acts like a temporary ( 6 months entry clearance visa).
Cost: Free, but there are associated costs such as collection of biometric data fees.
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With regard to travelling around europe, for the non-EEA national it is a bit more complicated. It is often suggested on here that it is a good idea to travel with a copy of your marriage or civil partnership certificate ( especially if the non-EEA is travelling alone, but also when travelling with the EEA national) and check the individual country's policies such as Shengen countries etc.
