Let us consider potential voting systems:
This is the system initially described. Simply put, the option with the most votes wins. Using this system would be a terrible idea since it would split the leave vote multiple ways, and you would very possibly end up with a decision that a minority of people voted for. It would trigger cries of betrayal from leavers immediately, and the result would likely not be respected. This will not happen.
This avoids vote splitting. Everybody would be able to rank the options. If there is no majority, the least liked option on first preferences would be eliminated, and those ballots' second preferences would be used. Repeat until a majority is found. This avoids vote splitting, and only requires one election. There are some issues with this voting method, including some bizarre tactical voting possibilities (see the wiki article on it here) but generally, it seems the fairest possible option for this. One of its main advantages is its simplicity. Other (potentially better) systems are more complex to compute, and so are more open to allegations of corruption as the general electorate may not be able to easily work out how the result was reached.
Two-Round Runoff Election
In this version there are two election days. On the first, all options are available. Then the top two are put head to head on the second. This is essentially a more expensive, less representative version of IRV. It is, however, even simpler, and it favours options which do very well on first preferences. Some people see that as more representative of people's true wishes, and it is more familiar to voters used to plurality systems. In a 3 option referendum, it would play out very similarly to IRV. The only legitimate difference would be the added expense of two separate election days.
While there are many other voting systems, most require more complex assessment to determine the victor. This would lead to questions of the legitimacy of the result, since people like to be able to immediately tell how their vote was counted. While systems such as Schulze or Borda Count may provide more representative results, perceived opacity in their computation is such that in my opinion, their use is highly unlikely in such a circumstance.