Edited based on new information provided
The most important thing to start with is: what resolution DAQ do you need? 16 bit is fairly standard, cheaper ones will be 12 or 14 bit. more expensive ones will be 20 or 24 bit.
Based on the specs you provided, Firstmark series 173-176, the conversion is 165 mm = supply voltage. Max supply voltage is 35VDC, but you could use anything. You didn't provide the min frequency you are interested, so let's just assume you need all the way down to 0 Hz, i.e. needs to be DC coupled. Most basic DAQ systems would be able to read -10V to 10V. You could get something that would read up 35V, you'll need something more expensive and complicated, so just assume you are keeping it simple and use 10V supply voltage.
A 16 bit ADC would set +32768 = 10V, and -32767 = -10V (note 2^16=65536, and we are using half that range for positive voltages and half for negative, hence 65536/2=32768... note that as I'm assuming DC coupled above, half the voltage range is unused... i.e. the DAQ system is setup to use -10 to +10, but you'll only be using 0 to 10V. If you can assume AC coupled you can use the whole range, but in that case the minimum frequency you can read would be a few hertz, won't get DC). So the smallest voltage you could read is 0.0003V.
With the assumption that 10V=165mm, this means the smallest displacement you could read is 0.005 mm. That would appear to meet your specifications. So a 16 bit DAQ should meet your needs, you don't need to spring for anything more expensive than that. On the other hand, a lot of cheaper systems might be 12 bit. Those will be 16 times worse resolution, i.e. minimum value you could read would be 0.08 mm. Probably would not work for you.
you were also asking about "40 kS/s", that's 40,000 Samples/second. That is not the maximum frequency that you can record however. General rule of thumb would be divide sample rate by 2.5 to get the maximum frequency you can record, which is called the "bandwidth". In this case 40k/2.5 = 16 kHz. You are referencing 7.2 kHz in the comments, which is less that I would have expected for a 40k sample rate. But since you said that you only care about signals at 300 Hz or maybe 1kHz anyway, this will be plenty for you.
while I'm thinking about it, another thing you should be looking at is whether the DAQ has built in anti-aliasing filters. Virtually all of the good ones do, but some cheaper ones do not. Unless you are 100% sure you know what you are doing, make sure you get one with an anti-aliasing filter.
I'll also say that most of the big DAQ manufacturers have pretty helpful sales engineers. Just call the company up and tell them what you are trying to do. They can probably point you in the right direction.