What distribution is the easiest to compress?
It's very easy to make fundamental mistakes on the topic of information theory, unless you have some PhD or alike in the field. That being said as far as I remember the following could roughly be stated about your question.

Considering a discrete probability and source model of iid, the most efficient compression of a source happens when the source has minimum Entropy (information) in it; i.e, its average codeword length (in bits) per symbol is minimum. Such a variable length code would have the highest compression and the most efficient coding to represent the source in a lossless manner.

Such a case would happen when one of the symbols of the source alphabet has a probability close to 1, and all other probabilities are close to zero. Such a distribution is said to be highly skewed. But I'm not sure if a unique minimum can be shown to exist unlike the case of maximum Entropy (minimum compression) which happens when all the symbols have equal probability.

On the other hand, you are talking about lossy Quantizers and probability distributions. PDF optimized lossy quantizer design is about finding the best input decision and output reconstruction levels for a given soure PDF such that the the expected quantization error (MMSQE) per given source distribution a minimum. And that's the Max-Lloyd quantizer for the scalar case. Rate-Distortion theory shall be invoked for various considerations here.

Merging these two concepts you would say that, for a given source power (or dynamic range) the one which required minimum number of quantization levels while still providing least possible quantization error (distortion) would be given by a source whose PDF is dense at a certain region. In that case you would put a few fine quantizer levels at those dense signal positions and then use larger step size levels outside of that region, which would still provide minimum expected distortion.