Sharepoint - How to change 'Welcome Page' on the basis of logged in user or group?

It's not possible OOB, but you can do the following:

• Create blank welcome page and put script editor web part on that page
• Put below script into the script editor:

function AutoRedirect() {
    var clientContext = new SP.ClientContext.get_current();
    var currentUser = clientContext.get_web().get_currentUser();
    clientContext.load(currentUser);

    var userGroups = currentUser.get_groups();
    clientContext.load(userGroups);
    clientContext.executeQueryAsync(function(){
         var groupsEnumerator = userGroups.getEnumerator();
          while (groupsEnumerator.moveNext()) {
             var group= groupsEnumerator.get_current();               
             if(group.get_title() == "Group 1") {
                 window.location.href = _spPageContextInfo.webAbsoluteUrl + "/Pages/page1.aspx"
                 break;
             }
             //etc...
          }

    }, function(err){
        alert(err);
    });
}

SP.SOD.executeOrDelayUntilScriptLoaded(AutoRedirect,'sp.js');

The code above checks if user belongs to a SharePoint group and automatically redirects to preconfigured page. This script is more efficient, becasue it doesn't iterate over all groups and users, that's why working faster.

function IsCurrentUserMemberOfGroup(groupName, OnComplete) {

        var context = new SP.ClientContext.get_current();
        var currentWeb = context.get_web();

        var currentUser = context.get_web().get_currentUser();
        context.load(currentUser);

        var allGroups = currentWeb.get_siteGroups();
        context.load(allGroups);

        var group = allGroups.getByName(groupName);
        context.load(group);

        var groupUsers = group.get_users();
        context.load(groupUsers);

        context.executeQueryAsync(
                function(sender, args) {
                   var userInGroup = IsUserInGroup(currentUser,group);         
                   OnComplete(userInGroup);
                },
                function OnFailure(sender, args) {
                   OnComplete(false);
                }
        );

        function IsUserInGroup(user,group)
        {
            var groupUsers = group.get_users();
            var userInGroup = false;
            var groupUserEnumerator = groupUsers.getEnumerator();
            while (groupUserEnumerator.moveNext()) {
                var groupUser = groupUserEnumerator.get_current();
                if (groupUser.get_id() == user.get_id()) {
                    userInGroup = true;
                    break;
                }
            }
            return userInGroup;
        }
}

Usage:

//Usage
function DoesCurrentUserBelongToGroup() 
{
  IsCurrentUserMemberOfGroup("Group A", function (isCurrentUserInGroup) {
    if(isCurrentUserInGroup)
    {        
        location.href = "https://siteurl/pages/Page1.aspx";
    }
  });
  IsCurrentUserMemberOfGroup("Group B", function (isCurrentUserInGroup) {
    if(isCurrentUserInGroup)
    {   
        location.href = "https://siteurl/pages/Page2.aspx";
    }
  });

}
ExecuteOrDelayUntilScriptLoaded(DoesCurrentUserBelongToGroup, 'SP.js');

There is no OOTB way to do that, what you can do is add a script editor webpart/content editor webpart on the default home page of portal and use above code to redirect users based on which group they belong to.

Reference - Check if user belongs to group

This is not only possible but I've done exactly as you describe completely out of the box, without a shred of JavaScript needed.

Here's the basic approach:

1. Create a custom list to use for the redirect.
2. A single line of text field houses the landing URL (Title is fine).
3. Create a calculated column to where the output generates a simple HTML redirect using the destination the user placed in the Title field.
4. Make the calculated column type as number or SP wil will display the code instead of rendering it.
5. Change permission on list items for each group who has a separate landing page.
6. Place the custom list on the welcome page, showing only the calculated column with an item limit of one.
7. This allows your Group A/B users to redirect to the secondary page because they can only see the one list item redirecting them to their custom page.