I will not claim myself to be any kind of authority on runes. IM NOT! But I do know most runes by memory, and I have done quite a lot of research online, reading rune stones.
The thing is, that a thousand years ago, there doesnt seem to have been any sort of general agreement on how the rune should look, which one to use, or even how words should be spelled!
However, one thing that is certain, is that most rune carvings found in Scandinavia are of the Younger Futhark. Maybe the Elder Futhark was just not ever that well known in its time, or the objects didnt survive the test of time, as they were older.
For some reason the people back then at some point decided that having only 16 letters were better than 24 (as in the Elder Futhark). I personally find this very strange. Especially many of the vowels disappeared, and you just have to use another letter to replace it.
For instance, there is no o in Younger Futhark, so you might use u instead. And there is no e so you might use i or a instead. Also, there is no v or w, which makes it hard to spell viking, so you spell it uiking instead.
I found a few rune stones which use the word brother.
Please note this when reading the rune inscriptions on Wikipedia:
Latin transliteration is letter for letter translation.
Old Norse transcription is what they meant to write, had they not been forced to replace letters with others.
http://en.wikipedia.org/wiki/Varangian_runestones#Vg_197
On this one from Sweden, brothers is spelled bruþr (That is bruthr. I do not know if this word is really plural or singular, as I do not know any old Norse grammar).
Bruþr is
ᛒᚱᚢᚦᚱ
<- Runes are written here, they might not be visible on phones, tablets, or some computers.
http://en.wikipedia.org/wiki/Varangian_runestones#.C3.96land
On this one, also from Sweden, brother is spelled bruþiR (That is bruthiR. Note that upper case R is not the same as a lower case, but I do not know why).
BruþiR is
ᛒᚱᚢᚦᛁᛦ
http://en.wikipedia.org/wiki/Ingvar_runestones#S.C3.B6dermanland (scroll up to U Fv1992;157)
Lastly, also from Sweden, brother is spelled bruþur.
bruþur is
ᛒᚱᚢᚦᚢᚱ
As you can see, there really are no standards when it comes to runes!
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Your Elder Futhark example spells BROTHERS, its all there. Im not really sure about the s, I believe its from the younger, but I might be mistaken there. But as I said earlier, there was no definite way of how they wrote their runes back then.
The Younger Futhark one says BRĄTHARS. The Ą seems to be more related to a than o, but since there is no actual o, Ą could work. Though using two us might be a little more authentic somehow.
In conclusion, there is no real correct way to spell it. If you are going for something as authentic Viking as possible, you should probably stick to Younger Futhark, as this is what they were known for using.
That said, I personally prefer Elder Futhark. I simply think it looks better, and youll have a better chance of using accurate letters. Amon Amarth use Elder Futhark exclusively in their artwork as well
(Though writing this post has actually made me realize that the missing/replaced letters in Younger Futhark are really quite charming!)