How exciting another baby girl on this thread! And that's such a lovely way to find out, congratulations.
Pregnancy in the heat we've had sounds tough, must've intensified the nausea somewhat... Have you found the sickness has got better in your second trimester so far?
As far as things to get,
Definitely a good travel system, we went to John Lewis to try some out and it was amazing how much some of them just didn't feel right. We went with the Silver Cross Cove which I can't fault - the cove 2 has just come out with a folding bassinet which I do wish we had!
Nappy caddies - we have one in the living room and one in the bedroom and it's just so helpful to have everything to hand and easy to store away. And in each nappy caddy we just have some nappies, some nappy rash cream, wipes, cotton pads and a spray bottle of water (so we're not using wipes all the time), spare change of clothes.
Clothes - I found it difficult to work out how much of each size to buy at the beginning when you don't know exactly how big the baby is yet. Our 25th centile baby didn't ever go in newborn clothes as she was so long, luckily we hadn't bought loads of newborn size clothes. She was in up to 1 month sizing for a bit, and I know of quite a lot of babies who have gone straight into 0-3 months. Maybe have a few of each, and Vinted is your friend.
We use dog poo bags instead of nappy bags, waaaay cheaper. We also use a puppy pad on top of the changing mat which helps absorb any free wees or poos that happen before you've put a nappy on 😅 it's saved us having to wash our sheets a few times now (we usually just change her on our bed rather than a full on changing table, but you'll find what and where works for you with all that)
One thing I would add is we haven't done her nursery yet. They sleep in your room until at least 6 months so we've kept what will be her room as the spare room. It just means we can keep the spare bed a bit longer which was so helpful at the end of pregnancy and the early newborn days where we could sleep in separate beds and get a better sleep.
Overall we bought a lot of it quite late on, there are loads of things that you don't necessarily need but you might suddenly find you do need something, in which case you'll either go out and buy it or Amazon prime it. For example one week in I realised I'd need to start pumping, we didn't have an electric pump so husband popped out to Argos and got one, job done. Most of it's not as urgent as it feels like it is