Contribution based is based only on your National Insurance contributions and takes no account of savings or your partner's earnings etc. This is only paid for a maximum of 26 weeks.
Income based JSA is a means tested and depends on your savings and household income. you can stay on this for a long as you qualify, so unless you get alternative income or get a job you continue to qualify. There is no set length of time for Income Based JSA and you can remain on it until you find work.
The first 3 days of a claim are waiting days and are not paid.
Depending on your circumstances you can also receive Housing Benefit or Support for Mortgage Interest (after 13 weeks) and a host of other reliefs.