What they said.

Find a bike in your budget that fits you. A (relatively) recent alu bike would be a good bet, just beware of older alu frames - I've had three crack, but they were all over ten years old. I still ride a NOS QR Kilo PR from 1998, and am not noticeably slower than my P2C, but the Cervelo is certainly more forgiving on the rough chip seal of NZ roads.

Aero frame is nice, and hydro forming alu makes them better than round tubes like my old QR, but most aero resistance is from the rider so getting a dialled in aero (and comfortable) position, and a frame that allows you to achieve that is key.

Not sure how easy to spot crash damage on carbon if you went for that secondhand. I'm sure wise folks here would guide you. I just bought an old Trek OCLV from the 90's for cheapness, just because I like them. It may well expolde underneath me, which I understand is what carbon does. Probably.

Stop worrying about frame material. It hardly matters at all.
A carbon bike is not automatically better than an alloy one.
Carbon allows for low weights and complex shapes. But there are light and aerodynamic alloy frames too and I'm sure there are poor carbon bikes. While carbon fibre does have advantages in many areas, the obsession with using it for every possible part of a bike is a fashion thing, borne out of ignorance and marketing.

A good alloy bike will be just fine and well worth having to avoid screwing around with your road bike.