Everything was fine until Hawkworld, when the silver age Hawks, Katar and Shayera arrived on Earth in the post Crisis era having just been teamed up (instead of being husband and wife before-hand.) Then things got even more messed up when the Hawks n the Modern era (before Hawkworld) were revealed to be stand-ins until the Invasion. Finally, Zero hour came and merged the new Modern Katar with all of the Hawkmen throughout time… After that, It just gets more convoluted no matter how many times they try to correct it. I love the current series, don’t get me wrong!..But, really, the genie escaped the bottle a long time ago.
Your best bet is just to read each new series as it comes along and hope they don’t do a reality shifting event in the middle of the run.