Here's what I suggest:
On the registration page, add a field where users need to enter a special code to complete registration and make the code as an image (or at least as something robots cannot process easy). This will prevent robots from constantly signing up to new accounts with bogus information.
Next, perform basic email validation to make sure the format is correct.
Next, strip the email address the user entered and verify the domain part is correct and if it is, have your server automatically send an email to the new account holder asking him/her to return to a special section of the site where he/she enters a special registration code assigned to him/her to complete registration.
Also, to save database space (I'm assuming registration info will be stored in one), ask users to complete registration within a limited time period or they will have to start over. If the time is up then relevant data from the database can be removed. I suggest setting the time period to at least one day.
If you are unable to do this, then you may need to find a better plugin that has the functionality I described.
And whatever you do, play with the website on localhost and make as few modifications on the live server as possible. This means make all changes at once on localhost if you can then upload everything at once to the live server.