Short length windowed sinc filter
The following is all assuming we are interested in Finite Impulse Response (FIR) filter design.

The cutoff frequency is not really the determining factor in the filter length. The 3 main things that determine the filter length are: the amount of passband ripple, the amount of stopband attenuation and the relative size of the transition band, i.e., the size of the band going from the passband to the stopband. Cutoff frequency will affect the design if it is really close to 0 Hz or half your sampling frequency.

The smaller the size of the transition band the longer your filter is going to be. To specifically answer your questions.

The sinc filter design is largely by trial an error to achieve your desired specifications. You play with the length of filter, the type of window used, and the filter cut-off to try to meet your specifications. So it may not be the most suitable in terms of trying to meet your spec. That said, it will give you an idea of the size of filter that would be required. Other design techniques are likely to require filters of similar lengths.

Regarding the transition width and sampling frequency, as I mentioned above it is actually the opposite. The smaller the transition width, the longer your filter is going to need to be.

One alternative, is to actually downsample your signal to reduce your sampling frequency. Since you are attenuating all signals above 70 Hz, why not just use decimation? The advantages of this technique are:


Reduced computational load
The filters used can be much smaller because they can have larger transition widths.
If really needed, you can upsample to get the data back to the original sampling rate using the same filters you used for the downsampling.


The main disadvantage is that your overall design is a bit more complicated. A good reference for this is "Multirate Signal Processing" by Crochiere and Rabiner.

If you are looking for the smallest filter lengths, then using the Parks–McClellan algorithm based on the Remez exchange technique has the shortest filter lengths for meeting passband ripple and stopband attenuation levels.