I think it would be much more useful if the email sent to admins could be customized to include a new user's user name, email address and IP address instead of a link to login. I'd certainly like to see this immediately and know whether I have a potential problem spammer on hand...
Have you modified the default templates in aMember? I thought it did what you are suggesting by default. This is what mine looks like: Code: New payment completed: Product: {$product.title} Amount: {$config.currency|default:"$"}{$payment.amount} Period: {$payment.begin_date|date_format:$config.date_format} - {$payment.expire_date|date_format:$config.date_format} User details: Username: {$user.login} Email: {$user.email} Name: {$user.name_f} {$user.name_l} -- Best Regards, {$config.site_title} {$config.root_url}