Setting values of a sn-choice-list is different from sn-record-picker where we pass to the field an array of a single object together with its displayValue and value - something like c.recordPicker = [{"displayValue": "test", "value": "testValue"}].

In sn-choice-list, it's more straightforward. You just have to assign the field a value itself from its existing options.

HTML

<sn-choice-list 
  field="c.mychoice" 
  sn-model="c.mychoice" 
  sn-options="c.mychoicelistoption" 
  sn-value-field="myChoiceValue" 
  sn-text-field="myChoiceDisplay" 
  sn-items="c.mychoiceoptions">
</sn-choice-list>

Client Script

c.mychoiceoptions = [{
    myChoiceDisplay:"Choice 1",
    myChoiceValue:'choice1'
},
{
    myChoiceDisplay:"Choice 2",
    myChoiceValue:'choice2'
}];

c.mychoicelistoption = {
    hideSearch: true
};

c.mychoice = "choice1";

As seen, you simply have to assign a valid value within c.mychoiceoptions based on your mapped field in sn-value-field which in this case should be taken from c.mychoiceoptions.myChoiceValue.