Cheapest Solution for Gapped Teeth?

The most cost effective way to correct a gap between two teeth is bonding. Material that is the same color as your teeth that is added on each side of the tooth.

I agree with the other doctors. Orthodontics or bonding are the most effective (and cost-effective) treatment to close your gap. If the crowding on the lowers is significant, you may want to use ortho. You may also have those teeth slightly recontoured (reshaped) for better appearance. A good cosmetic dentist will likely be able to close the gap between your teeth without removing tooth structure--and without a result that 'continues to fall off.'

The best way is to have an orthodontic evaluation. For minor tooth movement, there are multiple options, not necessarily braces. You may be a candidate for a retainer or Invisalign. Other than that some may suggest bonding to close the gap, which may le less costly and faster, however not a great choice. The bonding will most likely fall off, discolor or take away too much of your sound tooth structure.
The most important fact is to do it right so that bigger problems do not arise later on.
Good luck!

Your best route is of course orthodontics treatment, however, if finances are an issue consider bonding between the front teeth. A good cosmetic dentist can close that gap in one appointment and address all your esthetics concerns.
Best regards.