die Wahl
choice
The possibility or process of deciding between two or more options.
Du hast die Wahl zwischen dem roten und dem blauen Kleid.
You have the choice between the red and the blue dress.

choice / election
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choice
The possibility or process of deciding between two or more options.
Du hast die Wahl zwischen dem roten und dem blauen Kleid.
You have the choice between the red and the blue dress.

The noun 'die Wahl' (choice/election) is directly connected to the verb 'wählen' (to choose, to elect). Understanding the verb helps you work out the different meanings of the noun.
Wir müssen einen neuen Klassensprecher wählen.
We have to elect a new class representative.
In the meaning 'Entscheidungsmöglichkeit' (choice/decision option), 'Wahl' is often used with the verbs 'haben' (to have) and 'treffen' (to make). 'Die Wahl haben' means that options exist, while 'eine Wahl treffen' describes the active process of deciding.
Beim Nachtisch haben Sie die Wahl zwischen Eis und Kuchen.
For dessert, you have the choice between ice cream and cake.
The expression 'die Qual der Wahl haben' humorously describes the difficult situation of having to choose between many good options.
So viele tolle Reiseziele! Wir haben wirklich die Qual der Wahl.
So many great travel destinations! We really are spoiled for choice.
You can recognize the political meaning from words like 'Partei' (party), 'Kandidat' (candidate), 'Stimme' (vote), or 'wählen gehen' (to go vote). In this context, it always means a political vote.
Welche Partei hat die letzte Wahl gewonnen?
Which party won the last election?
The expressions 'erste Wahl' (first choice) and 'zweite Wahl' (second choice) are fixed phrases for describing quality. 'Erste Wahl' means the best option, while 'zweite Wahl' refers to lower quality or an alternative.
Dieses Hotel ist für unseren Familienurlaub die erste Wahl.
This hotel is the first choice for our family vacation.
possibility
'die Wahl' and 'die Möglichkeit' both have to do with options. 'die Wahl' emphasizes that you are deciding between several things or that there is a selection to choose from. 'die Möglichkeit' can simply be an opportunity or a possible option, even if you are not actively deciding yet. Learners often confuse the words because both can fit when talking about alternatives. In practical terms: if the focus is on deciding, 'die Wahl' fits. If it is about an opportunity or option, 'die Möglichkeit' fits.

Im Restaurant habt ihr die Wahl zwischen Fisch, Pasta und Salat.
At the restaurant, you have the choice between fish, pasta, and salad.
Mein Nachbar hat die Möglichkeit, seine Kinder früher von der Schule abzuholen.
My neighbor has the opportunity to pick up his children from school earlier.