I agree with your comments about option #3 being insecure.
As for programming either #1 or #2, option #2 is easier to program but #1 isn't much harder and both are probably about as secure as each other.
Whichever option you choose, you can also consider making it more secure by including requests for personal information (that you obtain during registration) as part of the forgotten password process.
I've programmed systems where you have a username and to get a new password you have to enter both your username and your email address. You can get sent a reminder of your username but the main point is that someone probably won't be able to guess your username and your email but if you do it just on email, there's less secure.
Secret questions are an approach to the personal information part. I personally think they don't offer a lot of value as people tend to choose questions that many people will either know the answer to, be able to guess or be able to find out. It is better than nothing however so long as you use it in conjunction with an already relatively secure method.
Obviously the more of this you do, the more programming work it is.
The simplest method is:
- Have a "remind me of my username" link (enter email). Don't tell the user if an email was sent or not because people can use that to find out if an email address is of a member. Always tell the user to check their inbox for the reminder email but only send it if someone is a member; and
- Require both username and email to get sent a new one-time password. That password should only last an hour or so. When the user uses it, they should be forced to change their password immediately.