I'm thinking of getting a laptop to play keyboard live using Ableton Live, and I'm wondering what I could get away with? I don't want to spend more than a few hundred, but I want to be able to play with a fairly nice latency. How powerful would a laptop need to be to do this?
I don't use Ableton in a live setting (yet), but I do use the software daily on a couple different computers so I can get you going in the right direction. The gold standard for DJs and live performers seems to be the Macbook Pro but I'm guessing since you don't want to spend much this will be above your price range (same for me, and I prefer PC anyway so I've been looking around for a good laptop to run Ableton as well).
Basically, you want a multi-core processor (Intel i5 or i7 would be ideal), at least 4GB of RAM (8 or more would be preferable), a SSD hardrive for speed (depending on if you use a lot of samples you can get away with as little as 128GB but I would prefer at least 256 or up to 500GB for an SSD). Also, USB 3.0 for connecting newer/faster audio interfaces. Most of these specs come standard on the $500+ laptops these days, it is really a great time to be in the market as the prices on hardware are getting very low and you can get a lot for your money. I won't go into specific models/brands, but if you follow the above guidelines you can get something that will cover your needs. Also keep an eye on battery life, depending on your setup you may want to have the option to play a gig without having the plug the laptop into the power outlet.
If you want to go under $500, you are going to have to skip on one or more of the above specs. If you aren't using samples you can probably get away with a 7200 RPM Hard drive (non-SSD), and maybe 4GB of RAM with an i5 processor. Also I don't like or need a touchscreen for my uses, so if you are the same you can save some money by forgoing the touch-capabilities.
Also, aside from just checking the software minimum requirements, see what Ableton has to say on the subject: https://www.ableton.com/en/articles/what-computer/