I read this thread, and wasn't sure about whether to really say anything, as I just haven't been in your situation. We did live in an apartment for about 7yrs, but I was not alone. It was my wife and myself, and our 1yr old son when we moved in. Our daughter was about 2 when we left. Almost the entire time, I was the sole income. So, it was similar in many ways, and even tougher in some. We did prep then. Of course we had less space with more people, and very little "expendable income".
We never did gardening, as we didn't have any sun-filled windows. Trees close to the buildings on the sun side prevented most of the sun from coming in. We just stocked what we could.
You really have to prioritize. Space and income are limited, so without prioritization you will end up without something you need. As for the stove, I'd still have one and stash it under everything else in a closet. Stash the fuel the same. I know the landlord can more or less invade at will, but generally they won't dig through your stuff. Therefore, you don't want to make your stocks look suspicious. You can cook with a camp stove inside if you open windows for ventilation.
You also want to think about whether you would stay or not. Like mentioned, if you're leaving, all you need is enough to get you to your leaving point, plus some. Put the rest somewhere else.
Be careful about your preps. There are a lot of people crammed into a close area in the apartment complexes, and most will not prep. Combined with an apartment is hard to defend, and you have a potential problem. Ideally, you get your neighbors to prep also. Then you find a place to have a community garden. If you have any friends who have an area of yard they aren't using, a deal may be struck where you garden in their yard, and they get some of the rewards.
Start with what you are preparing for, from most likely to least likely.
Then, you can figure what you need to get through what you are preparing for.
Just do it a little at a time, as much as you can.
It's tough in small spaces. You have to prioritize, and you will have to be organized.

Remember, just a little bit is way ahead of the rest. With a weeks food, you are already staying safe at home while those who ran out after 2-3 days hit the street. You said you had 6 months, and that is a very good start, beyond many. With 6 months of food, I'd start looking at other areas. Water. Medical. Defense. Heat. Can you stay warm enough in the winter?