No toilet shut off valve in the NYC apartment

I'm not a professional plumber (though I did work on water treatment systems for several years), but in my opinion what you did is fine.

Gate and globe (stop) valves are prone to corrosion and generally wear out over time. Ball valves are much more durable and reliable. I've seen many, many old stop valves that are leaking or don't shut off properly, or more often, leak as soon as you open/close them after they've not been touched for years. I can't say the same for ball valves - I've seen many that were installed for many years and still worked. I can even think of a couple where the outside looked totally corroded, and though it took a lot of force to turn (and sometimes a replacement handle), they still reliably shut without leaking.

On top of the reliability, the fact they use a 1/4 turn (instead of several full turns) and a quick glance tells you whether it's open or closed, ball valves are just vastly superior to gate and globe valves for almost all residential applications. Worth the extra dollar or so they cost.

The only thing they are not as good for is applications where you want to limit/control the flow rate (such as an outside tap or sample port). They can still do that, but are harder to finely adjust, and especially when one hasn't been opened for a long time and is a bit stiff, tend to suddenly give and open to full blast (I've been sprayed while trying to take water samples many times).

Knowing where the water lands gets you in the area, but what you really need to know is where the water came from. Is the tank cracked, is the supply line failing, is there a bad connection on either end of the supply line, or is the valve itself going.

If the tank is cracked, you'll have to buy a new one, and it's a large project if you're not used to working on basic plumbing jobs or are skirmish around an open toilet.

A bad supply line can be easily replaced and it's even easier if it's just the washers.

A bad valve may just have some dirt or buildup in it that will be fixed by opening and closing it once or twice with water running through it (an empty toilet tank). Though keep in mind any dirt may then get in the toilet valve and could cause it to run slowly until you clean it out. If that were to happen, just post another question. It could also be the packing material in the valve, which I've never touched on this type of valve. If that's the case, you may be able to minimize it by opening the valve all the way. If the valve is too far gone, you'll likely need a blow torch and solder to replace it. This can be a DIY job, but if you get in over your head, the water for the whole house will need to be shutoff until you can get a plumber out.