You need pull-up resistors on the outputs (or whatever load you want to drive).
Inside the ULN2003 there are darlington transistors with an open collector, so without some external circuit the output will not be pulled up to some higher voltage.
The COM pin is connected to a freewheeling diode for each transistor, so you can connect it to the positive rail to protect against overvoltage, for example for inductive loads.
Since the display includes the Ilitek ILI9320 controller, then your interface requirements are much lower, as the microcontroller no longer has to interface directly with the TFT and instead only talks to the controller chip via a simple interface: either SPI, which takes six wires: RS, CS, CLK, MOSI, MISO and RESET. Or you can use an 8080-compatible parallel interface which takes 13 wires: an 8-bit data bus, and RS, CS, WR, RD and RESET. (There are options to use larger data-buses, up to 18 bits, but I don't recommend that for a low end microcontroller.)
There are two optional interfaces in which the microcontroller generates all of the clock signals (VSYNC, HSYNC and DOTCLK); you don't want to do that since it would require a high-end controller.
So just about any microcontroller will do, however you need to have enough flash memory to hold whatever static items you want to display; for example if you are going to be displaying text then you will need to allocate arrays to store bitmaps for whatever fonts you will use. Even a small font can take 60KB.
One of the advantages of this controller is that includes 172,800 bytes of RAM, which is enough to store 320*240*18 bits. However it is not double-buffered, meaning that when you write to the RAM, it will immediately show up on the screen, and if you updating a lot of the screen, it will be noticeable.
Best Answer
The purpose of the watch dog timer is to reset the MCU should a hardware or software fault occur. It does this by generating an interrupt at certain intervals and if the interrupt does not get serviced in a specified amount of time, resets the MCU.
In general, the result of a reset mid way through your program will depend on what exact hardware the MCU is controlling and what state it is in.
For the clock you are building, I wouldn't worry about this since any type of failure will not be critical. I would say feel free to disable the watch dog timer to save power but since this is not a hobby/diy project, discuss the impact of this with your client.