TableView that sorts either by clicking on the column headers or by selecting a column from a combo box.

ComboBoxSortableTable.java

import java.util.Arrays;
import java.util.Collections;

import javafx.application.Application;
import javafx.beans.property.SimpleStringProperty;
import javafx.beans.property.StringProperty;
import javafx.beans.value.ChangeListener;
import javafx.beans.value.ObservableValue;
import javafx.collections.FXCollections;
import javafx.collections.ListChangeListener;
import javafx.collections.ObservableList;
import javafx.scene.Scene;
import javafx.scene.control.ComboBox;
import javafx.scene.control.ListCell;
import javafx.scene.control.ListView;
import javafx.scene.control.TableColumn;
import javafx.scene.control.TableView;
import javafx.scene.control.TableColumn.SortType;
import javafx.scene.control.cell.PropertyValueFactory;
import javafx.scene.layout.BorderPane;
import javafx.stage.Stage;
import javafx.util.Callback;

public class ComboBoxSortableTable extends Application {

    @Override
    public void start(Stage primaryStage) {
        final BorderPane root = new BorderPane();
        final TableView<Person> table = new TableView<Person>();
        table.setItems(createData());
        final TableColumn<Person, String> firstNameColumn = new TableColumn<>("First Name");
        final TableColumn<Person, String> lastNameColumn = new TableColumn<>("Last Name");
        firstNameColumn.setCellValueFactory(new PropertyValueFactory<Person, String>("firstName"));
        lastNameColumn.setCellValueFactory(new PropertyValueFactory<Person, String>("lastName"));       

        table.getColumns().addAll(Arrays.asList(firstNameColumn, lastNameColumn));
                
        root.setCenter(table);
        
        final ComboBox<TableColumn<Person, ?>> sortCombo = new ComboBox<>(table.getColumns());
        
        // Generics hell... much nicer if you can use Java8 lambda expressions
        final Callback<ListView<TableColumn<Person, ?>>, ListCell<TableColumn<Person, ?>>> cellFactory = new Callback<ListView<TableColumn<Person, ?>>, ListCell<TableColumn<Person, ?>>>(){
            @Override
            public ListCell<TableColumn<Person, ?>> call(ListView<TableColumn<Person, ?>> listView) {
                return createListCell();
            }
        };
        sortCombo.setCellFactory(cellFactory);
        sortCombo.setButtonCell(createListCell());
        sortCombo.valueProperty().addListener(new ChangeListener<TableColumn<Person, ?>>() {
            @Override
            public void changed(ObservableValue<? extends TableColumn<Person, ?>> obs,
                    TableColumn<Person, ?> oldCol, TableColumn<Person, ?> newCol) {
                if (newCol != null) {
                    table.getSortOrder().setAll(Collections.singletonList(newCol));
                    newCol.setSortType(SortType.ASCENDING);
                } else {
                    table.getSortOrder().clear();
                }
            }
        });
        table.getSortOrder().addListener(new ListChangeListener<TableColumn<Person, ?>>() {
            @Override
            public void onChanged(Change<? extends TableColumn<Person, ?>> change) {
                while (change.next()) {
                    if (change.wasAdded()) {
                        sortCombo.setValue(table.getSortOrder().get(0));
                    }
                }
            }
        });
        
        root.setTop(sortCombo);
        
        final Scene scene = new Scene(root, 400, 600);
        primaryStage.setScene(scene);
        primaryStage.show();
        
    }
    
    private ListCell<TableColumn<Person, ?>> createListCell() {
        final ListCell<TableColumn<Person, ?>> cell = new ListCell<>();
        cell.itemProperty().addListener(new ChangeListener<TableColumn<Person, ?>>() {
            @Override
            public void changed(
                    ObservableValue<? extends TableColumn<Person, ?>> obs,
                    TableColumn<Person, ?> oldColumn, TableColumn<Person, ?> newColumn) {
                if (newColumn==null) {
                    cell.setText(null);
                } else {
                    cell.setText(newColumn.getText());
                }
            }
        });
        return cell ;
    }

    public static void main(String[] args) {
        launch(args);
    }

    private ObservableList<Person> createData() {
        return FXCollections.observableArrayList(
                new Person("Hugo", "Lloris"),
                new Person("Danny", "Rose"), 
                new Person("Jan", "Vertonghen"), 
                new Person("Michael", "Dawson"),
                new Person("Kyle", "Walker"), 
                new Person("Sandro", "Raniere"),
                new Person("Paulinho", "Maciel"), 
                new Person("Gylfi", "Sigurdsson"), 
                new Person("Andros", "Townsend"),
                new Person("Aaron", "Lennon"), 
                new Person("Roberto", "Soldado"));
    }

    public static class Person {
        private final StringProperty firstName;
        private final StringProperty lastName;
        

        Person(String firstName, String lastName) {
            this.firstName = new SimpleStringProperty(this, "firstName",
                    firstName);
            this.lastName = new SimpleStringProperty(this, "lastName", lastName);
        }

        public String getFirstName() {
            return firstName.get();
        }

        public void setFirstName(String firstName) {
            this.firstName.set(firstName);
        }

        public StringProperty firstNameProperty() {
            return firstName;
        }

        public String getLastName() {
            return lastName.get();
        }

        public void setLastName(String lastName) {
            this.lastName.set(lastName);
        }

        public StringProperty lastNameProperty() {
            return lastName;
        }

        @Override
        public String toString() {
            return firstName.get() + " " + lastName.get();
        }

    }
    
}

In Java 8, the mess that is creating and setting the cellFactory reduces just to
sortCombo.setCellFactory(listView -> createListCell());