To answer your question, simply, for you I first need to point out:
You have not specified the explicit case or cooling system, making it very difficult to even speculate on your question
You have not provided information on your CPU or GPU temps - it would be best to measure your CPU and GPU temps to see if they are currently sufficient.
You have not specified what games you are intending to play.
Now, none of that really matters. As I said in my comment your question is rather difficult to answer correctly as there are way too many variables to take into account:
How does your PC sit? Depending on how your PC sits would first determine how well the case can 'breath', how much air-flow the device receives and overall, how susceptible it is to shock (as in, being kicked etc.)
How frequently do you run your PC? Most components have a general life expectancy, many Intel SSD's have a read/write life as an example.
For your reference, here are some blogs you may be interested in:
Now, I can relate your question to a typical car related question:
How many miles will I get out of a tank of fuel in my car?
Is there an accurate answer to this question? No. It all comes down to user-related variables. Here are 7 easy tips to improve the lifespan of your PC.
Lastly to summarize on your question -
IF your CPU temps are higher than normal (you can simply google '
<your cpu> temp' on Google to find out) than I'd suggest getting the water cooler before and case (PSU and Motherboard are not as important).
IF your CPU temps are normal and well, I'd consider hold off and do them all at once if feasible, because needing to migrate your motherboard twice (for a case) is not going to do wonders for it, try and make it one smooth transition.