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My problem is that the following tree produced with tikzpicture squeezes my nodes way too close together, as you can see in the picture below. I have been trying to use level distance to move the them further apart, but I can't seem to figure out the right way to use it.

Please excuse me if this seems simple. I'm still new to the world of Latex. To be honest, I'm quite proud I got this far.

begintikzpicture
tikzsetgrow'=right,level distance=60pt
tikzsetexecute at begin node=strut
tikzsetevery tree node/.style=anchor=base west
Tree[.Gesamtes Lösungsgebiet [.Hintergrundnetz ]
 [.Airframe
 [.Zelle und Tailboom ]
 [.Kufe und Streben (x2) ]
 [.Hauptrotormast ]
 [.Leitwerke ]]
 [.Rotoren
 [.Hauptrotorblatt (x2) ]
 [.Heckrotorblatt (x2) ]]]
endtikzpicture

In order to save some horizontal space, I have introduced a linebreak in the first node (As stated on page 3 of the tikz-qtree documentation this can be done using the align option.) I have also increased the value of level distance :

documentclassarticle
usepackagetikz
usepackagetikz-qtree

begindocument

begintikzpicture
tikzsetgrow'=right,level distance=100pt
tikzsetexecute at begin node=strut
tikzsetevery tree node/.style=anchor=base west, align=center
Tree[.Gesamtes\ Lösungsgebiet [.Hintergrundnetz ]
 [.Airframe
 [.Zelle und Tailboom ]
 [.Kufe und Streben (x2) ]
 [.Hauptrotormast ]
 [.Leitwerke ]]
 [.Rotoren
 [.Hauptrotorblatt (x2) ]
 [.Heckrotorblatt (x2) ]]]
endtikzpicture
enddocument

If you want to individually influence the level distance you can use tikzsetlevel 1/.style=level distance=150pt see page 5 of the manual for more information.

With forest is simple. With l sep you can define distance between levels independently from length of node text:

documentclassarticle
usepackage[edges]forest

begindocument
beginforest
for tree = 
 grow' = 0,
anchor = west,
 l sep = 11mm,
 s sep = 3mm,
edge path = noexpandpath[forestoptionedge]
 (!u.east) -- (.west);
 ,
 
[Gesamtes Lösungsgebiet
 [Hintergrundnetz]
 [Airframe,
 before computing xy=s/.average=ssiblings
 [Zelle und Tailboom]
 [Kufe und Streben (x2)]
 [Hauptrotormast]
 [Leitwerke]
 ]
 [Rotoren
 [Hauptrotorblatt (x2)]
 [Heckrotorblatt (x2)]
 ]
]
endforest
enddocument