If you have your lathe sitting in the "lounge" of your 1 BR apt then I assume it is a mini-lathe. These are not known for power, rigidity or speed and while carbide will work, it is not the best choice for these little lathes, as the guys have noted. I can see why you don't want to grind tools inside your dwelling and if you can't do it outside then you have to buy your tooling.
My first choice would be to have someone on the forum grind some tools for you. There are definitely some of them who are capable of grinding really nice tools for you; all you need to do is hone them and keep them sharp. The advantages are that they will be ground to work well with your small lathe, will last for years and are cheap.
If you prefer to buy inserted tooling then listen to
@Nogoingback and get the AR Warner stuff. HSS inserts work well, even on a mini-lathe, and you can use carbide inserts in their tool holders if you wish. This is a higher priced option but will work better for you than carbide.
Brazed carbide tooling works well if you buy good tools and keep them sharp with a diamond stone, which can be done by hand. If you go this route, I suggest Micro 100 tools.
Last option, to me anyway, would be inserted carbide tools. These tools work on a small lathe but are nowhere near the performance of a good HSS tool. If you go for these, look for the SCLCR/L tool holders that take CCMT or CCGT inserts.
The performance of your lathe is greatly dependent upon the cutting tools you use. At this point you have no options but to buy your tools. Choose wisely.