Which 3D printer controller should I use?
Controller boards
Please note (this is not to bash) that RAMPS shields are not the top of the line printer controller boards, investing in a more modern printer board platform (preferably not a clone of a known board), e.g. a 32-bit board might be a better solution.
Any board with at least four stepper drivers should be sufficient (you can use the two Z steppers in parallel or in series), some boards even offer two Z stepper output connectors controlled by a single stepper, e.g.:

No worries if the board doesn't have two Z stepper connectors, you can buy dual stepper breakout boards, e.g. a parallel solution:

Alternatively, an extra stepper driver can drive the extra Z stepper; this requires a board with at least 5 stepper drivers then, the Z2 stepper would then be connected to the E1 extruder driver. The firmware needs to be aware of using 2 stepper drivers, so in Marlin (depending on the version) set Z_DUAL_STEPPER_DRIVERS or assign a value to NUM_Z_STEPPER_DRIVERS .
Anet heatbed
The Anet heatbed is notoriously known for fire accidents/burning caused by the underrated connectors (the connector itself is not rated for 10 A!), also the connector should require proper strain relief. The best solution is to solder the heat bed wires directly to the backside of the connector (which is what I did on my old Anet A8 printer, I used multiple pins soldered together, both the outer 2 pins on either side), an example from the web (downside is that they only used a single pin) shows this principle (with solution for cable/soldering stress relief using a tie-wrap):

A final notice for connecting heatbeds is to use proper cables; silicone cables of proper gauge (silicone wires are very flexible, e.g. AWG 14) should be used. Also, never solder the ends and put them under screw connectors on the printer board, instead, use ferrules or proper sized fork terminal connectors.
MOSFET Band Aid
In case the MOSFETs on your boards are underrated, you can use external MOSFET boards to relieve the shield/printer board from the high currents. Note that the bed requires the most current (about 10 A), for the hotend this will not be required, the current draw is much lower, the onboard MOSFETs are rated for those loads.