Congratulations!
I also have an Aygo and we have a mamas and papas sola2. The carry cot fits in the back seat and the rest in the boot. We got it as a bundle with car seat, isofix base etc. There are often offers in their Huddersfield factory outlet or if you attend a parents to be event.
Don't buy mattresses or car seats second hand but everything else is fair game.
Don't buy loads of clothes, you will get more than you can imagine in gifts! Get some basic vests and sleepsuits - so comfy for baby and easy to get on and off!
Aldi do the cheapest disposable nappies that I have found and they are actually really good quality - I prefer them to other brands. No need to buy pamper etc. Don't stock up on loads of nappies as you don't know how quickly your little one will change sizes. We have just gone into size 2 at 13 weeks but we needed size 0 initially. My nephew went into 2s at 6 weeks.
The other thing to consider may be reusable nappies - they do work out cheaper long term for many of you get birth to potty training ones, but it's a large expense initially.
We used a basic Moses basket for our little one, rather than super fancy cribs etc, mainly due to space but it's worked absolutely fine and they will not be in it forever!
Facebook marketplace and eBay is where I got most of our second hand bits but also check if there are any nct second hand sales near you too.
We started changing our spending habits before the money dropped so it wasn't so much of a shock (and we saved more in those 'practice months' for the tighter months