4 Days in Vienna: Which city/transit pass is best + how do student discounts work for foreign students?

Hello!

My gf and I (both university students from Italy) are planning a Vienna trip for April. We will be staying for 4 days and 3 nights. We are currently planning our itinerary and trying to figure out the best way to get around without spending too much.

We have a couple of questions:

1. Which transit/city pass makes the most sense?

We are in doubt between regular public transport tickets (like the 72-hour ticket or the weekly pass from Wiener Linien) vs tourist passes like the Vienna City Card or the Vienna Pass. We plan on using public transport every day and want to visit the main attractions (Schönbrunn, Belvedere, Hofburg, Albertina, etc.). What is the most cost-effective combination for a 4-day stay?

1. Student Discounts & Valid ID

We would like to take advantage of student discounts for museums and attractions. What kind of proof is accepted in Vienna? Is a standard certificate of enrollment from our Italian university (or our digital university app) enough? Or do places strictly require a physical card with a photo, like an ISIC (International Student Identity Card)?

Thank you so much in advance!