"Mexico is paying for it indirectly through the new trade agreement"
That's firstly rather disputed -- because, after all, the new Trade Agreement has not yet come into effect -- and secondly, very different from what Trump was saying during the campaign. A classic bait-and-switch, and you've fallen for it.
With respect to the staff, you'd need at least some of them anyway even if you did have a wall, so the cost is almost by definition going to be bounded by that of the wall. And, again, your argument signally fails to recognise the progress already made over the last decade, when limited investment in border security, including staff alongside some minimal fencing, led to a 75% reduction.
The wall is not necessary, and Mexico is not now paying for it.