"We are buying a trip to a different country."
Translation:Kupujemy wycieczkę do innego kraju.
'podróż' - journey (an act of travelling from one place to another)
'wycieczka' - excursion (a short journey or trip, especially one taken as a leisure activity)
Of the two, 'journey' seems more general. You can say e.g. 'Journey by train took 2 hours' - 'Podróż pociągiem trwała dwie godziny'.
Hmm, technically perhaps it might be slightly weird if you think about it deeply because "podróż" is indeed more about the time spent while travelling however the simple fact that I as a native speaker automatically used this word in the above sentence means that it's not uncommon for us to switch between "wycieczka" and "podróż" in many contexts. After all, had it been a round the world trip, we'd more likely have said "Kupujemy podróż dookoła świata".
Hmm... "podróż" and "wycieczka" may be quite similar, but I wouldn't say that I can buy a "podróż" in a travel agency. It means "a travel" or rather "a journey".
"wycieczka" would be rather "a trip" and you can certainly buy those.
As for "Chcę idę", that's like "I want I am going" or something like that :/ "chcieć" needs either a noun phrase or a verb in infinitive. So it would be "chcę iść", only that... "iść" means that you will only walk during this trip, so let's say you are in some village in the mountains and "idę na wycieczkę po górach" - I will walk there.
"chcę jechać" is more probable, as you will need some vehicle.