Suicide and homicide are categorized as intentional deaths and you can find statistical rankings of countries by intentional death rate.
As far as guns being the most lethal method of suicide, the right-to-suicide advocates use suicide attempts in their stats as opposed to suicidal gestures which are more a call-for-help than a serious suicide attempt.
Methods of Suicide
Rank / Lethality / Method
1. 99.0% Shotgun to head
2. 97.0% Cyanide
3. 97.0% Gunshot of head
4. 96.4% Shotgun to chest
5. 96.4% Explosives
6. 96.2% Hit by train
7. 93.4% Jump from height
8. 89.5% Gunshot of chest
9. 89.5% Hanging
10. 78.5% Auto crash
11. 77.5% Household toxins
12. 76.5% Set fire to self
13. 73.0% Structure fire
14. 71.0% Carbon Monoxide
15. 70.0% Hit by truck/auto
16. 65.5% Electrocution
17. 65.0% Gunshot of abdomen
18. 63.0% Drowning ocean/lake
19. 58.5% Stab of chest
20. 51.5% Cut throat
21. 49.4% Overdose illegal drugs
22. 23.0% Plastic bag over head
23. 21.5% Drowning bathtub
24. 21.5% Drowning swimming pool
25. 12.5% Stab of abdomen
26. 12.3% Overdose prescription drugs
27. 6.0% Overdose non-prescription drugs
28. 6.0% Cut wrists/arms/legs
General suicide studies from different sources do give different results. JJ Card gave suicide by gun as 91.6% effective. Farberow and Shneidman had it 84.7%. Hawaii Dept of Health had it 73%. Those studies gave suicide by hanging as 77% to 88% effective.
The decision to commit suicide precedes the choice of means. As the experience in Japan illustrates, their suicide rate is extremely higher than that of the United States in a culture where very few people ever owned guns, no tradition of owning or using guns and the current laws are extremely strict. Some of the Japanese suicide methods, including combinations of household poisons, are hazardous to people other than the person choosing suicide. So restrictive gun laws don't mean no suicide since there are other equally effective means, or if the person is seriously willing to try multiple times.
National Academy of Sciences, National Research Council, "Firearms and Violence: A Critical Review" (2004) Chapter 7 Firearms and Suicide
http://www.nap.edu/openbook.php?record_id=10881&page=169
[FS/S is ratio of firearms suicides to total suicides]
In Box 7-2, for example, we present the results of a simulation conducted by the committee. In this Monte Carlo simulation, we study the relation between the suicide rate and FS/S as a proxy for gun ownership, but we derive very different results than those reported by Miller et al. (2002a, 2002c). In particular, we find a negative association between the suicide rate and FS/S: in this simulation, if FS/S is a good proxy for ownership, gun owners are less likely than nonowners to commit suicide.
(How does the number of suicides or effectiveness of shooting as a means prove any effectiveness of gun control? Suicide advocates list "Overdose by illegal drugs" as 49% lethal. How can that be? We not only have drug control laws, we are in the midst of a War on Drugs. If legal control on things controlled bad behavior by people, how could there be enough suicides by overdose on illegal drugs to get a percentile of effectiveness?)