Effect of different downsampling rate on EEG signal
Given that you have removed all signal content above 10 Hz, your 20 Hz sample rate will be identical to the minimum sample rate based on the Nyquist sampling criterion.

If you instead use 5 Hz, you can only represent a bandwidth of 2.5 Hz and, e.g., a signal appearing to be at 2 Hz might have been a 3, 7 or 8 Hz signal as well (meaning that you can not distinguish between a signal at any of those frequencies after the downsampling). This is caused by aliasing.

Using 60 Hz would be clearly feasible but will consume more storage of the signal. The possible benefit might be that later processing may be simpler as the signal does not cover the whole signal band. However, this depends on which processing is required later. Also, while the processing in itself may be simpler, there are more samples to operate on so the total complexity may not be reduced.