Hi Luison,
I have gone through your question and following is the answer :

Apex Class: DevCommunityQ1 

global with sharing class DevCommunityQ1 implements Database.Batchable<sObject> {
    global Database.QueryLocator start(Database.BatchableContext Bc){
        String query='SELECT ID,NAME,Next_Class_Update__c,RecordTypeId FROM CONTACT';
         return Database.getQueryLocator(query);        
    }
    global void execute(Database.BatchableContext Bc,List<Contact> contList){
        list<Contact>updateContactList = new list<Contact>();
         Id recordTypeChildId = Schema.SObjectType.Contact.RecordTypeInfosByName.get('Child').RecordTypeId;
        if(contList!=null){
            for(Contact cont:contList){
               if(cont.RecordTypeId ==recordTypeChildId){
            cont.Next_Class_Update__c=Date.today();
            updateContactList.add(cont);
               }
            }
        
        }
        system.debug('-----> updateContactList'+updateContactList);
        if(updateContactList.size()>0){
            update updateContactList;
        }
    }
    global void finish(Database.BatchableContext Bc){
        
    }
}

Apex Class : ScheduleDevCommunityQ1

Apex Class : ScheduleDevCommunityQ1

    global with sharing class ScheduleDevCommunityQ1 implements Schedulable {
    global void execute(SchedulableContext ctx){
        Database.executeBatch(new DevCommunityQ1());
    }
}

Developer Console execute this Script :

System.Schedule('Next Class Update','0 0 0 1 7 ? *',new ScheduleDevCommunityQ1());

Explanation:
To write Apex Scheduler code you first need to write Batch class (check my DevCommunityQ1 Apex class).The Batch class have 3 parts or you can say, It is divided into three Sections.

 Section 1: global Database.QueryLocator start(Database.BatchableContext Bc)
 This section is used to write the query in String format.
 Database.getQueryLocator(query) will execute your query and return List to Section 2.
 
 Section 2: global void execute(Database.BatchableContext Bc,List<Contact> contList)
 This section will allow you do all the manipulation 
 
Section 3: global void finish(Database.BatchableContext Bc)
This section is just use for cleanup purpose.You have to another Apex class that will schedule your Batch class (Go through the ScheduleDevCommunityQ1 Apex Class) , but you haven't executed any of your Code.  Now What you need to do is in Developer Console you have to execute the following Script: 

System.Schedule('Next Class Update','0 0 0 1 7 ? *',new ScheduleDevCommunityQ1());

The System.Schedule method takes three arguments: a name for the job, an expression used to represent the time and date the job is scheduled to run, and the third argument will be object of the your Schedule class because it has the object of the Batch Class.
Hope it will work for you.
 
 Regards,
 Akshay