Exit Single Market: the UK will seek leave the EU Single Market in a “clean” Brexit because being a member of the market means accepting the Four Freedoms including the free movement of people in the EU, something that is seen as a red line following the UK Brexit vote.
Free Trade Deal: whether realistic or not, the UK will seek to negotiate a free trade deal with the EU in the 2 year period of negotiating to leave the EU after triggering Article 50 of the Lisbon Treaty (expected in March 2017 with Brexit in 2019). Transitional measures could be in place for some industries e.g. Financial Services until a trade deal is in place.
Customs Union: since being a member of the EU Customs Union would prevent the UK from entering into other trade deals, the UK will also seek to leave this (unlike e.g. Turkey which is party to the Customs Union although outside the EU).
Parliamentary Vote: whatever negotiated position between the EU and UK is reached will be put to a vote in both Houses of Parliament in Westminster. The question is would a rejection of a Brexit deal by Parliament be seen as frustrating the will of the people?
“No deal better than bad deal”: if the UK gets no deal agreed with the EU, the UK will be free to change its economic model to become a low tax haven outside the EU and presumably suck away business and tax revenue from the EU. This would be a nuclear option.