We were/are in the exact same situation. 6.5 months and we're still in the one bed but hoping to move soon! We had:
A Moses basket and stand (now repurposed as toy box in the living room). That was replaced by an Ikea cot and we had to put a couple of bits from our bedroom in storage to make that work.
For storage we had this - www.argos.co.uk/product/7013227?istCompanyId=a74d8886-5df9-4baa-b776-166b3bf9111c&istFeedId=c290d9a9-b5d6-423c-841d-2a559621874c&istItemId=ixilatttl&istBid=t&&cmpid=GS001&_$ja=tsid:59157%7cacid:844-913-7556%7ccid:9567867118%7cagid:99275631118%7ctid:aud-641224041017:pla-889386694449%7ccrid:423233944798%7cnw:g%7crnd:16986449476231793868%7cdvc:m%7cadp:%7cmt:%7cloc:9045999&utm_source=Google&utm_medium=cpc&utm_campaign=9567867118&utm_term=7013227&utm_content=shopping&utm_custom1=99275631118&utm_custom2=844-913-7556&gclid=Cj0KCQjwpdqDBhCSARIsAEUJ0hMv4kR0hzbh2Id26gyR3a7nUM7tQfDhGugwtuvX7NjSte26oy8ONeIaAj9LEALw_wcB&gclsrc=aw.ds. Much smaller footprint than a changing table and it fits all her clothes, bedding and muslins with spare nappies and wipes underneath this/the cot.
We just used a changing mat on bed or floor. Highly recommend getting some kind of caddy to carry changing stuff around in. Very cheap on Amazon.
We started out with just a sling but she wasn't initially a fan so we got a pram as well. We have the Ergobaby Metro, which is the only one I found with a foldable bassinet that baby doesn't have to be strapped into. We've been very happy with it.
If you don't have a tumble dryer, highly recommend a heated clothes rail for the never-ending laundry. On which note, you will need tons of outfits in whatever is your first size as you will go through multiples per day, but way fewer in the next size up as peeing, therefore accidents, get less frequent. In terms of bedding, we used velcro swaddles and then sleeping bags so the two lovely cellular blankets I bought are the only thing that was hardly used (though useful to have at least one for pram/impromptu naps when they're already asleep and you haven't got them into sleeping bag etc).
We got a Skip Hop Pronto instead of a changing bag - can carry it around in whatever bags you already use, or clip to the pram.
From about two months, a baby gym will be your most used item - loads available on eBay and they can generally be folded and stashed behind the sofa so don't begrudge it the space.
If you get to this stage - we spent ages searching for the perfect foldable high chair and eventually settled on the non-folding, ubiquitous IKEA Antilop because the footprint of most is still so big when folded that you probably wouldn't bother folding it down in a small flat.
I know it's frowned upon on Mumsnet but we would not be without our nappy bin - the outside bin is miles away, no way were we visiting it regularly with a newborn. Similarly, we have a folding baby bath stand from Ok Baby and find it much easier than our attempts to bathe her in the sink in the early days (it just lives propped against the wall in the bathroom). In the first month or so you can bathe them infrequently and get in with them, but that's not a solution in the medium term.
Don't spend lots on a sling before they're born as not all babies are fans. Ours is reconciled now that she's able to look around but I would have been gutted if I'd spent a lot in the early weeks/months when it was a total screamfest. Happily, a stretchy wrap is your best bet for newborns and also cheapest and most compact option so start with that.