I lived on a first floor 1 bed flat with DS1 until he was 2. Moved when v heavily pregnant with DS2 into a 2 bed.
Get a lightweight, folding buggy. We have a bugaboo bee and it was so good for when we had a flight of stairs to contend with. I've heard the ant is also very good.
Get the best sling you can afford and become its best friend. It will be soooo much easier to sling the baby up and down the stairs. It's hard work at first but your body gets used to it. Id also recommend contacting your local sling library to get thier advice on which sling may suit your body.
Get rid of anything you don't need and do it now before the baby comes. Because you will not have the time to sort it with a newborn. DP and I made the mistake of leaving jobs to be done for after the DS1s arrival.. they never got done!
The baby born bouncer is good and folds flat, our DCs have bobbed away in that happily for a long time until at least 6months.
Don't worry about having to make a trip to the garden, we have the same in our current place, you get used to jt and plan accordingly. Just always keep your bag stocked with nappies, wipes, a change of clothes and a large muslin and you're pretty much set for most disasters.
DS2 still sleeps in our room and we had a side sleeper for a long time (hes just in the bed with me now) so I guess keeping the other room as a guest sounds sensible.
Make the most of the free childcare/help from your parents!! I'm jealous as we never got any help at all.
I think the main thing we living in a small place is to live minimally and consider anything coming in to your flat very carefully. Especially with baby stuff as you'll be made to feel like you have to have certain things that in reality won't get used. Buy second hand and sell forward stuff as and when necessary.
Good luck and congrats!