I think it's worth examining something like the Bracero program, from the 60's, and seeing if a more modern version could be implemented.
I also think things like the existing E-verify system, or a similar means of assessing worker eligibility could be more cheaply implemented, with the onus on employers to mandatorily use it.
Finally, I think there should be a beef-up of the checks and policing of legal visa overstays, which account for a large portion of the illegal immigration anyway.
These measures would support each other, and I'd estimate they'd be considerably cheaper than a wall.
Similarly, there is nothing wrong with beefing up border security to some degree. I just don't see a physical wall which then needs to be maintained, and can be breached in remote locations as a sensible spend of funds.
Your thoughts on those?