When I first started traveling to Japan, and particularly via KIX, I usually worked backwards from my desired arrival at the airport to figure my train times. Some folks like to get to the airport a couple of hours before flight time, others cut it closer or allow even more time. When I have lounge access, I like to get there at least 2 hours before flight time and spend a little while decompressing in the lounge. From there, I work back 75 minutes for the Haruka and find the nearest departure time that gets me there at those times. That is my last possible departure. Then, for safety's sake, I'd plan on the Haruka just prior to that. In that way, I'd have a fall-back if something happened and I missed the earlier one. If I didn't miss it, I just had some extra time in the lounge. If I missed TWO departures, I'd still get to the airport over an hour before my flight and be able to make my flight if I hurried.

Using Hyperdia, you can look up all the train departures, travel times and arrival times at the airport station to get a very accurate plan, including fall-back options. Just start with the arrival time that leaves you a couple of hours before your flight and work backwards to find the best departure time(s.) Use Kyoto to Kansai International Airport and choose "Arrival" instead of the default "Departure." When you have a listing for the JR Haruka, you can select "Interval Time Table" (under the train number) to see all the other options for that train.

From Kyoto Station, once you get on the Haruka, there is no way to get off at the wrong station as the line terminates at the KIX station. The train makes a couple of stops along the way to pick up passengers in Osaka. Just don't get off before you get to the airport. The announcements are in English.

As an example, my United flights usually departed about 4:45 pm. Two hours means arriving at the airport by 2:45. The 1:15 pm Haruka arrives at 2:34, so that is my primary train. If I want to be extra safe, I plan on taking the 12:15 train, which puts me at the airport 3 hours in advance. If I miss that train, the 1:15 gets me in over 2 hours before my flight. If I miss THAT, I still have the 2:15 that will get me there over an hour before my flight, which means hurrying and skipping the lounge.

The Haruka starts running at 5:46 am and runs twice per hour in the early morning and once per hour after 10:15 am. If that is not enough, there are plenty of other train connections to the airport but most of those require a change somewhere like Shin-Osaka. If you are nervous about connections, I'd recommend just staying with the Haruka as you can't miss your stop.

That was a VERY long-winded way to say that Kyoto to KIX is very stress free and easy to make almost any international departure.

EDIT: I see we were all typing at the same time, said approximately the same thing and gave the same advice - some just a lot more concisely.