Browsing on LCSC learned me that the cheapest board to board connection is a through hole header/socket connection.

Pitch

2.54mm is the most widely used and easy to solder

Number of contacts

2x5 & 2&6 pin configuration get you the most bang for the buck when taking into account the cost of the mated connection, i.e. male+female part.  They only cost $0.01 more than the 1x5 or 1x6 configurations.  The benefit of having extra pins is also having extra ground return paths.  This reduces the HF-current loops of the SPI communication.

PCB Mounting

Through hole components are cheaper, but require an extra PCB process: wave soldering.

SMT components are more expensive, but can be reflow soldered with the other SMT parts.  The PCB supports both connector types.

Mating height

This might be a bit of a bummer if you really want low profile.  The male header requires 2.5mm height, while the female socket puts 8.5mm on top of that.  This amounts to a 11mm inter-PCB distance.

Mechanical fixation

The LED PCB must be supported on both sides to keep it stable.  Adding a few additional header/socket connectors on the corners might do the trick.

Another option was to use plastic self retaining spacers. Wuerth has these in their product line.  These require a free height of 1.9mm under the LED matrix.

Instead I opted for SMT studs.  They can be reflow soldered with the rest of the SMT components.  These studs have an internal M3-thread, so they provide for an firm screw connection to the base board.  They're electrically conductive, so can be used to return ground current, a benefit to keep EMI under control.