I am a city dweller, and the answer depends on a lot of factors, that include the construction type of the building, where your apartment is located in the building, and the noise tolerance of your neighbors (which may change with the level of outdoor noise).
Two examples from my experience:
1. I was living in (former East) Germany a couple of years ago, 4th floor of a concrete building (even the separation walls were concrete, the stuff was tough as a bunker), in a quiet neighborhood, practicing in a room with hardwood floors, 1 shared wall and neighbors above and below, using a 15" cabinet driven by a 125W solid-state amp. Even at low volume, my 70yrs-old neighbors upstairs would hear it (and love it, saying it reminded them of the time they were playing in a band in the Free Socialist Youth), and my middle-aged neighbors two floors up were hearing it too (and complaining about it. A lot). So, it was mostly headphones.
2. I am now living in a condo in a city center in California, typical wood frame on a concrete base, so more like a duplex situation really, in a fairly busy part of town. My practice room has carpet, one shared wall, I practice with a 12" cabinet driven by the same 125W amp. Never had a problem with the neighbor (who is a student).
In both cases, I play at low volumes, and restricting my playing time to what I think are reasonable hours (9AM to 9PM). Outside of those hours, it's headphone time.
I guess that what I am trying to say is that there is unfortunately no general answer, and that it will depend on the particulars of the situation.
In any case, I would suggest you find something that sounds good, and that's convenient. There's been a lot of good suggestions above for amps (I am in the tube pre-amp + solid-state power amp + cabinet camp).
For headphones I heavily recommend the BOSS Waza-Air bass. I like to stand when I play and I hated having wires running from my bass to the amp, and another back from the amp to the headphones. With the Waza-Air, you plug the dongle in the bass, put the headphones on, and you are good to go. If you want effects, or back-up tracks, or a tuner pair it with your phone or tablet. It's been a game changer for me.
Good luck in your search for a good amp, and remember to look at the Classifieds here, there are some good deals to be found!
