Hey there! I've been working with second hand pushchairs recently so can help with this. There are a few things I'd recommend keeping in mind.
The main thing is to make sure it's operational and there aren't any major signs of wear and tear. Check the brakes, harness, and the overall sturdiness to ensure it's up to snuff.
Test out how easy it is to fold and unfold, maneuver it around a bit, and see if the adjustable features work fine. You don't want to be fumbling with a wonky pushchair when you're out and about in the streets.
Make sure it's nice and clean. Take a peek at the fabric, frame, and accessories to see if they're in decent shape. You don't want to deal with sticky stains or funky odors. Also, consider how easy it'll be to clean if it needs a little sprucing up.
Ask about its history! Find out how old it is and how much use it's seen. It's good to know if it's a well-loved veteran or a barely-touched gem.
Oh, and don't forget compatibility! Especially if you are going to buy a specific car seats, make sure it's going to be compatible.
Also might want to do a quick online search to get a sense of what it originally sold for and compare prices with other similar models. You want to make sure you're not overpaying for a second-hand pushchair.
Trust your gut instincts, my friend! If something feels off or if you have any questions, don't be shy to ask the seller! Safety first, find one that suits your lifestyle, and happy pushchair hunting!