Setting the FilePath property is correct. Be aware to set this string exactly as it appears in the Folder dropdown field of the DnnFilePicker. That is, if you want for example to have the Images folder as default, then you have to set the FilePath property to 'Images/'.

To define the default folder within the module settings instead on codebehind you can add a dropdown displaying the portal folders this way:

Settings.cs:
var moduleSettings = mc.GetModuleSettings(ModuleId);
UserInfo user = UserController.GetCurrentUserInfo();
var folders = FolderManager.Instance.GetFolders(PortalId, "READ,ADD", user.UserID);
ddlDefaultImagesFolder.DataSource = folders;
ddlDefaultImagesFolder.DataBind();
ddlDefaultImagesFolder.SelectedValue = moduleSettings.GetInteger("DefaultImagesFolder", 0);

Settings.ascx:
<asp:DropDownList ID="ddlDefaultImagesFolder" DataValueField="FolderID" DataTextField="FolderPath" runat="server" Width="300px" />

This way you can save the FolderID within your settings.