If we're going to do it, it's got to be with troops - and, frankly, lots of them.
We've got two borders of about 2,000 miles each - that's 4,000 miles. At one person per mile, working normal hours, we'd need 16,000 people just on the borders - with NO administrators! (Yes, I know, no admin is an impossible dream).
Practically, if we want to actually take control of the border, we need 100,000 troops. Anything less than that, we're just playing the same silly games that have gotten us to the present point.
First, I wouldn't put our active duty guys on this mission. Its basically patrol duty. I would give Texas, New Mexico, and Arizona a huge increase in Guard personnel. Simply give a college education (4-years) to any 18 to 25 year-old kid to join the Guard for border duty for 8 years. You make sure that they can give 3 months of duty each year and you write it into the contract that they can't be taken for Iraq duty or anywhere else overseas. We'd get 100,000 kids joining the Guard down there in two months. After I hired that group, I'd go the retired military folks and offer them a state pension deal to wear the AZ guard uniform for 10 years and collect a small state pension at 65 years old ($8k a year would be enough to entice them because they already have the regular military pension). That would give you your entire force, at the lowest cost. And they would provide the best protection at the border.