Hi Achilles,
You can set a default container for creating Groups in Self Service. In order to achieve that, you will just need to define a setting called NewObject.Container on the Settings tab in Self Service Portal.
Please follow these steps to define this setting:
On the Server node in Self Service Portal, go to the Settings tab and click the Add button as shown in the screenshot below:

Add Setting dialog box appears.
Select NewObject.Container from the Key drop down list.
Specify the path to the Container in the Value field. Suppose, you have an Organizational Unit called User Groups which you want to set as the default container and your domain name is techworld.com, then you will need to configure the path to the OU as shown in the screenshot below:

Click OK
Save the changes by clicking the Save button as shown in the screenshot below:

Now launch the portal and login with any user. You will have a default container pre-populated and the Browse button will be grayed out as shown in the screenshot below:

Note: If this setting is not applied, Reset you IIS server and then launch the portal.
I hope this will help you achieve your desired functionality.