In all honesty I think I'd go for one of the maclarens that has a shoulder strap so that you can collapse the buggy, put it over your shoulder and still have hands free for baby/shopping. Not the most comfortable for a really small one so maybe get a sling or borrow something a bit more substantial for the first 6/8 weeks.
Have a look at Babyjogger City Mini GT. Very manouvreable on and off buses, and it does one-hand fold, and you can buy adapters and fit a carry cot or car seat. Realistically though, you're only going to be able to carry baby + one bag up 3 flights of stairs - is there anywhere you could store a collapsed buggy downstairs?
Just coming to say baby jogger city mini gt too! I bought when living in a lift-less flat, invaluable, still going strong 4 years later and about to take my 3rd kid!
You just have to think k about the order of things before you do them and you'll be fine! Eg. Baby and bags go up first, put in safe place, back down for buggy. On the bus - I've never had to fold my buggy but I'm always well prepared to be able to if needed!
I had this when my daughter was little. Also didn't have a car. To be honest, i went through a few different prams, travel systems and the issues were still the same. So just get the one you like best. Though I would suggest looking at something that has a higher under carriage basket and brake bar as these bang against stairs when bumping up and down. And something with bigger, sturdier wheels too would help.
I used to have to take baby out of pram, take her upstairs and put her in Moses basket. Then run back down for the pram. Same as going out - I'd run down with pram first, set it up. Then go back upstairs for baby.
But as she got bigger and wouldn't 'stay put', i just had to keep her in the buggy and bump her up and down the stairs in it.
When there was shopping on the handlebars, I kept her strapped in buggy downstairs (to stop buggy toppling backwards), take shopping up to flat, then run back down and bump her up the stairs.
Sounds a lot of hassle but it just becomes part of the 'going out' routine.
Have a look at the baby zen yoyo, they do a 0+ version. We have the original and it's a godsend for travelling, it folds down one handed and can be slung over the shoulder. It's incredibly light as well.
I'll just add - we have a silver cross pioneer and whilst beautiful, it's very heavy. I wouldn't want to carry it up any stairs and the car seat seemed much than a maxi cosi to me but I haven't checked.