As far as I can tell, using 'join' or the concatenation operator(.) are both reasonably fast; interpolation is slower than either. Of course, you would have to do a lot of joining for it to make any difference in the speed of your program.
If interpolation is more readable (which I think it is), you could always do this:

my $dir = $HOME.'/'.$first.'/'.$second;
[download]

for the extra speed boost. :-)
(Actually, that's kind of ugly, too. I would probably just interpolate.)

Impossible Robot