Hi,
The circuit seems OK provided you will connect the input clock to its drive to enter the input data.
The Carry in of the 4008 need to be connected, if no data for it then ground it. never leave a CMOS input not connected.
74573,74574 are TTL 8 bit latches, also 373 and 374 are 8 bit latches with different pin configuration. If you need only 4 bit you may use 74190 counter , just use the load function and forget the count, all the "S,LS,HC" etc.....
for CMOS use 4034 for 8 bit and 4029 counter/latch for 4 bit