What proportion of a padded FFT should be actual values For a given signal, I've been told that you can pad the vector with $0$s at the end to get a larger DFT, and as a result get more precision in frequency bins.


What are the limits to this approach? 
Is there a loss of accuracy when you do this?
Or if not, why wouldn't you just use a small number of points and pad with zeros all the time?
Be careful with this in thinking that you would increase your frequency resolution- you won't! Zero padding is very effective in iterpolating more samples between the samples you have, but it does not add any more information about the frequency content of your signal between your original bins.  You do not lose anything either.

The frequency resolution in all cases is $1/T$ where T is the time length of your data. 

Please see my answer at this post specifically for more details on zero-padding and how it works: What happens when N increases in N-point DFT