Durable nail type that works with these designs (no extensions)?

Thinking of my getting a manicure bit of a noobie when it comes to the diff nail types (e.g acrylic, dip, gel x, biab, etc).
I'm thinking of getting either this pink design with the cheetah prints or the cats eye ombre design (I think the latter would be cheaper?).
Although I'm not leaning towards getting extensions and and id rather be able to take them off at home. So what type do you think would work for the designs?

I was thinking of UV Gel overlay which I think is just something applied before the colors and design to keep it long lasting? And ofc there's shellac which is the cheapest for me but I heard it peels away and even chips after just a couple days 💔

Any advice is appreciated hehe