The safest bet if I have one male and one female is to add another male, correct?

Two females would most likely fight over the male?

Or will two males fight over the female too?

 

Or is the only safe to add 3 budgies of the same sex in a large cage?

The safest bet if I have one male and one female is to add another male, correct?

Two females would most likely fight over the male?

Or will two males fight over the female too?

 

Or is the only safe to add 3 budgies of the same sex in a large cage?

3 same sex would be best. Females rarely fight over a male but males will fight over a female.

It also depends on the temprement of the birds. I have had 2 males and 1 hen live quite happily together...

I believe its when the sexes are greatly outnumbered (such as one male to say 7 hens) that it can become quite dangerous for the male.

I've found that three in a cage seems to work best when one of them is a loner. Occasionally we've had a budgie who seems to have very little interest in the others, but the others aren't bothered by that budgie being there either. Otherwise they seem to pair up and then leave the third one out most of the time. I've seen this with both the gender combinations you're talking about. The only times I've actually had attacking it was always the hen that seemed to get attacked, and usually a hen who did the attacking too. But I've only done this a few times so others who have had a lot more budgies than I did will probably have a lot more experience to draw from

Two males will fight over a female, I've had that problem just recently and it was very distressing to see, they were brutal with each other, I certainly wouln't recommend it. All budgies have different personalities and you may be lucky to get two males and a female that get on fine but I know I wouldn't chance it again.