Recommended Advanced Combat Skills

The most important Advanced Combat Skills to obtain are: Offensive Combat 1, for a significant increase in skilling speed; Combat Efficieny 4, for its long-term AP savings; Defensive Combat 3, for a significant increase in survivability; Ambush Fallback 1, for the ability to retreat through a wormhole to make finding you post-ambush much harder; Timebombs I and II, for their general utility both offensively and defensively; Agility Boost 4; for an increase in survivability; a Weapon Spec 4, for the increase in damage; and Offensive Combat 3, for the significant increase in offensive ability. 

The recommended order to obtain Advanced Combat Skills is:

1. Combat Mastery
2. Offensive Combat 1
3. Combat Efficiency 1 (Optional)
4. Combat Efficiency 2 (Optional)
5. Combat Efficiency 3 (Optional)
6. Combat Efficiency 4 (Optional)
7. Defensive Combat 1
8. Defensive Combat 2
9. Defensive Combat 3
10. Ambush Mastery
11. Ambush Fallback 1
12. Ambush Fallback 2 (Optional)
13. Chronoton Collection
14. Timebomb II Construction 1
15. Timebomb II Construction 2
16. Timebomb II Construction 3
17. Timebomb I Construction 1
18. Timebomb I Construction 2
19. Timebomb I Construction 3
20. Boosts
21. Agility Boost 1
22. Agility Boost 2
23. Agility Boost 3
24. Agility Boost 4
25. Weapon Mastery
26. Weapon Spec 1 (Imperials should choose C, non-imperials should choose either EM or O)
27. Weapon Spec 2 (Imperials should choose C, non-imperials should choose either EM or O)
28. Weapon Spec 3 (Imperials should choose C, non-imperials should choose either EM or O)
29. Weapon Spec 4 (Imperials should choose C, non-imperials should choose either EM or O)
30. Ambush Endurance 1
31. Ambush Endurance 2
32. Ambush Endurance 3
33. Ambush Endurance 4
34. Offensive Combat 2
35. Offensive Combat 3

Once you have obtained all of the above Advanced Combat Skills, it is recommended to optionally obtain a second (or third) Weapon Spec, along with Cloaking Boost and Taming Boost if desired. The latter two skills are rarely useful and can be skipped entirely. The reason for delaying Offensive Combat 3 to the end is to reduce the overall damage dealt to the NPCs you are skilling on, to help them live longer and provide more gains in the long run.