ExploreCustomContactController.java

public with sharing class ExploreCustomContactController {
    public ExploreCustomContactController() {

    }

    @AuraEnabled
    public static Map<String, String> getFieldTypes(List<String> selectedFields){
        String objectName = 'Contact';
        Map<String, String> fieldTypeMap = new Map<String, String>();

        for(String field : selectedFields){

            Schema.DisplayType fieldType = Schema.getGlobalDescribe().get(objectName).getDescribe().fields.getMap().get(field).getDescribe().getType();
            fieldTypeMap.put(field, String.valueOf(fieldType));
        }
        return fieldTypeMap;
    }
    
    @AuraEnabled(cacheable=true)
    public static List<Contact> getContacts(List<String> selectedFields){
        String s = '';
        Integer i = 0;

        for(String field : selectedFields){
            if(i == 0){
                s+= field;
            }else{
                s+= ','+field;
            }
            i++;

        }
        String query = 'SELECT ' + s + ' FROM Contact';
        
        return Database.query(query);
    }

    @AuraEnabled(cacheable=true)
    public static List<String> getContactFields(){
        SObjectType contactType = Schema.getGlobalDescribe().get('Contact');
        Map<String,Schema.SObjectField> mfields = contactType.getDescribe().fields.getMap();

        List<String> sObjectDetailsList = new List<String>();
        for(String s : mfields.keySet()){
            sObjectDetailsList.add(String.valueOf(mfields.get(s)));
        }
        return sObjectDetailsList;
    }
}

ExploreReimplementDataTable.html

<template>
    <lightning-datatable
        key-field="id"
        data={fetchedContacts}
        columns={columns}
    >
    </lightning-datatable>

    <label>Select the fields you want to display in the Data Table</label>
    <select class="slds-select" name="optionSelect" multiple>
        <template for:each={wiredContactFields.data} for:item="field">
            <option key={field} value={field}>{field}</option>
        </template>
    </select>

    <lightning-button
        label="Looks Fine"
        onclick={handleSelectedFields}
    ></lightning-button>
</template>

ExploreReimplementDataTable.js

import { LightningElement, track, wire } from 'lwc';
import getContacts from '@salesforce/apex/ExploreCustomContactController.getContacts';
import getContactFields from '@salesforce/apex/ExploreCustomContactController.getContactFields';
import getFieldTypes from '@salesforce/apex/ExploreCustomContactController.getFieldTypes';

export default class ExploreReimplementDataTable extends LightningElement {
    @track columns = [
        { label: 'Id', fieldName: 'Id' },
        { label: 'Name', fieldName: 'Name' }
    ];
    @track selected = ['Id', 'Name'];
    @track fetchedContacts = [];

    @wire(getContactFields) wiredContactFields;
    @wire(getContacts, { selectedFields: '$selected' })
    wiredContacts({ error, data }) {
        if (data) {
            this.fetchedContacts = data;
        } else if (error) {
            console.log(error);
        }
    }

    handleSelectedFields(event) {
        //clean the array
        this.selected.splice(0, this.selected.length);
        this.fetchedContacts = [];
        this.columns = [];

        for (var option of this.template.querySelector('select').options) {
            if (option.selected) {
                this.selected.push(option.value);
            }
        }

        getContacts({ selectedFields: this.selected })
            .then(result => {
                this.fetchedContacts = result;
                this.handleFetchFieldTypes();
            })
            .catch(error => {
                console.log(error);
            });
    }

    handleFetchFieldTypes() {
        getFieldTypes({ selectedFields: this.selected })
            .then(result => {
                this.columns = this.selected.map(field => {
                    const dType = result[field];
                    if (dType === 'STRING' || dType === 'ID') {
                        return { label: field, fieldName: field };
                    } else if (dType === 'DATE') {
                        return { label: field, fieldName: field, type: 'date' };
                    } else if (dType === 'DATETIME') {
                        return {
                            label: field,
                            fieldName: field,
                            type: 'datetime'
                        };
                    } else if (dType === 'Integer') {
                        return {
                            label: field,
                            fieldName: field,
                            type: 'Integer'
                        };
                    } else if (dType === 'BOOLEAN') {
                        return {
                            label: field,
                            fieldName: field,
                            type: 'text'
                        };
                    } else {
                        return { label: field, fieldName: field };
                    }
                });
            })
            .catch(error => {
                console.log(error);
            });
    }
}