Some questions about buying a pre-owned xbox series s?

Hello! I'm kinda new-ish to gaming, I've played DMC 1-4, doom 2 and doom 2016 before (on a decade old work laptop my dad forgot to discard🥀). [irrelevant info] I've now converted that old lappy to a linux machine and i have a pavillon x360 13th gen i7, 16/512gb as my main laptop for college and coding and editing and stuff so I'm looking to buy a dedicated machine for gaming.

The thing is, since I'm a student I don't have much of an income, so I'm gonna have to convince my parents to buy me sumn so I'm looking for the cheapest possible option (under or close to 20-30K rupees)

What I've considered:

1. Pre-owned handhelds: used steam decks, rog allys and msi claws are fascinating options but pretty hard to find second-hand atm

2. Used PS4: The most budget option that can run games, but the games that I'm looking to play are kinda pricey on the playstaion store (dmc 5 is like 700rs on the xbox store and 2500-ish on the playstation store rn so that's the only thing keeping me from going for a used ps4)

3. Used ps5: Might somehow get this in-budget but the same issue as the ps4

4. gaming mini pc: one of those skullsaints thingies. not a fan.

5. regular gaming pc: out of budget :/

6. Keep gaming on the pavillon: it has an intel 13th gen i7, 16gb/512gb, and integrated iris xe graphics. It runs hot tho cuz hp, I've played on it before but connecting it to a tv and keeping it docked is a pain, especially with the shit battery. I'll just play the games which are not on the xbox on this one.

The games that I like to play/am planning to play: DMC 3-5, Doom 2016-dark ages, wolfenstein new colossus, resident evil, assassins creed, sifu, tekken, street fighter

So yes, I'm pretty set on a pre-owned xbox series S. I'm not gonna consider the series X because a series S can run most of these games and I'm not looking to do any hardcore gaming and I gotta keep things as cheap as I can :P

I'm gonna go to nehru place in june (it's like 2 metro stations away but i got endsems rn :/). Will I be able to find a better deal at Nehru place or online?

Also, any advice is much appreciated. ik I'm asking for too much for a device to play all these games under a budget of 30K but I'm broke so🥀

thankyou for reading all my yap🙏