The consensus from most e-bikers is that you need at least a 400w motor to get up a steep hill without pedaling. If you don't mind pedaling then a 250w motor is fine but just keep in mind that you probably won't be able to go on an entire ride without pedaling unless you live in a very flat area. For example, I have a 750w motor and I went on a ride today and never pedaled the entire time. It even carried me up a pretty steep hill.
Yes, there is a big difference in 24v, 36v, and 48v and that's speed and power. In order to use 36v or 48v, you need to have a proper controller that allows that kind of voltage. So you'll have to know what kind of controller that you are getting. I have two controllers and two e-bikes. One controller is a 48v 1000w controller so I can only use 48v batteries on it. I can't use 36v on that controller. It won't work right because of the low voltage cutoff setting. My other controller is a 36v - 72v controller which means that I can use any voltage from 36v to 72v. Also, if your controller says it's made for 48v, if you put more on it, you'll likely fry it.
But yeah, even with a 250w motor, you might go 15 mph with 24v but you might go 22mph on 48v so adding more voltage will increase speed and acceleration but it still might not be able to get up a steep hill without pedaling. Most people get at least a 400w motor. I like speed and power, though so you might want just a little bit of assist so the 250w motor might satisfy you just fine.
If you live in california, you can rent e-bikes for the day so you should go rent one and try it out and ask about how much power it is so you can have an idea what you like.