If you're going to follow Starting Strength, then the only equipment you'll need is a squat/power rack. Make sure to get a rack that can support the bar on the inside AND outside, that way you can do the overhead press without the top of the rack obstructing you.
First thing you want to address is safety: is the floor steel reinforced concrete, or is it just wooden flooring with beams? The latter is far less likely, but you should always check first just in case.
To get rid of sound there are several tricks you can do:
- Tell your neighbors. Telling them in advance will make them a lot less likely to report you for noise, and they can give you times to deadlift when they aren't at home.
- Use planks to disperse load. Get a piece of wood or similar material and put it at the base.
- Use free carpet samples. Get a bunch of those carpet samples and use them as added padding to absorb the deadlift.
- Buy a rubber mat. Yoga mats are not very thick, so look for larger mats used in gyms.
- Control the bar. The biggest thing you can do to minimize sound is control the bar on the way down, and never drop it.