STM32F407 CMOS or TTL or HC
Manufacturers put a LOT of effort into making sure ICs are compatible with other I/O standards so that you can interface them to actual hardware (otherwise, who would buy their stuff?). Some even go so far as to have like 20 different I/O standards supported on each pin (FPGAs usually have this sort of configurability).

Here's the output specification of your chip (from the datasheet):


And the input specification (FT = 5V tolerant pins, TTa = 3.3V tolerant IO):


For inputs, it should be able to take just about anything that can meet those levels (LVCMOS (3.3V, etc), probably HC when its run at 3.3V). For outputs, it can also meet 3.3V TTL.

If you're unsure if it will work well with the logic parts you have selected, I strongly suggest you read their datasheets. In general, any CMOS-based part should have zero issues. You may run into problems trying to drive 5V TTL (use a level shifter to 5V if you need to do this and find problems).

Here's some simple steps if you are concerned about I/O standards compatibility:


Check the output high level voltage minimum of the driving IC against the high level input minimum of the receiving IC. The driver should be greater than the receiver by at least a hundred millivolts or more (noise immunity).
Check the output low level voltage maximum of the driving IC against the low level input maximum of the receiving IC. The driver should be less than the receiver maximum by at least a hundred millivolts or more (noise immunity again).
Check that the driver's maximum output voltage is less than the recommended maximum input voltage for your receiving IC.
Make sure you are meeting any weird requirements of the driver, such as a minimum output load. It is likely there are no weird requirements, especially if you stick to regular modern CMOS or HC logic.
Make sure you are meeting any weird requirements of the receiver, like minimum input drive current. Same story as above, almost no weird requirements if you stick to regular and modern logic families.