Which of the following conjugations of viajar in my sentence is correct?
Espero que yo viajaré/viaje/viajaría a España.
I am focusing on Spanish from Spain.
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The correct one would be Espero viajar a España.
According to the Diccionario panhispánico de dudas
Cuando significa ‘tener esperanza [en que algo suceda] o creer que sucederá’, es transitivo y va seguido de un infinitivo o de una oración introducida por que: «Espero llegar a vieja sin arrugas» (Allende Eva [Chile 1987]); «Espero que todo te vaya bien» (Gala Invitados [Esp. 2002]).
This means that whenever the verb esperar means "to hope for [something to hapen] or believe that something would happen," you have to use the infinitive form.
Hope this helps!
At least in my (northern Spain) dialect the most natural way would be
espero + INFINITIVE
However, at least in my dialect, it would also be perfectly fine to use
espero + SUBJUNTIVE and not so uncommon to be honest...
I think "espero que yo ..." sounds weird/unusual/jarring to us Spanish speakers because "yo" is also the speaker themselves, so they already know as much as possible about "yo". Same with "desear/ansiar/añorar": "deseo que yo viaje a España" ---> "deseo viajar a España". Perhaps for the same reason(s) we do not have first person imperative.