Ok so I did a run with this squad and I have to say, the only Mech I found worthy of putting every single core in at the start was the Enhancing Mech. Everyone else could wait their turn for weapons upgrades.
I think the Mortar Mech could use a 2-core upgrade for Buildings Immune though because so many strategies were ruined by those buildings and a lot of artillery weapons eventually pick up a Buildings Immune power of some sort. Abe is definately a must for that Mech to be effective as well.
The Nanobot Mech is also useful but it's more like a Pulse Mech without two directions and it can shield buildings in front of it.
Now you could say that I could shield buildings, then drop the Mortar on the area but the Nanobot Mech is being used elsewhere to push things away. So maybe instead of a range increase or a close-range damage boost, Buildings Immune might be a better power.
The Enhancing Mech is insane though; however the Precharger doesn't seem to do anything on the first shot if you have +1 damage. I was expecting at least +2 damage right out of the gate; because it charges up a shot for +1 damage. So for two turns, you'd think it'd do 2 damage, then 3, then 4. So that probably needs looking into.