There is no single solvent known which dissolve all active ingredient present in mint. Selection of solvent depends on the type of active component you want to isolate. There are many specific solvent which dissolve specific type of compound. But generally diluted ENA [Extra neutral alcohol(Ethyl alcohol)/ different concentration of alcohol] are used for extraction of pharmaceutical active compound from plant like mint etc.
The best toxicity effect could be possible only if the compound is extracted in a high dielectric constant solvent such as water solvent, thus it will be of great benefit if the cyto-toxic compound is extracted in water.
Because the high dielectric constant will neutralized the opposite charges in the extract and gives the compound activity directly. This minimized the effect of other solvents effect on test organism.
However, it will not always the result, thus usually other solvents could be judged in experimentation.
I am not an expert with the solvent selection - I will leave that to those better qualified than I [although typically we see our customers use a hot water extraction and then an organic solvent extraction].
With regards to the freeze drying, water can be freeze dried, to get a good result you must make sure the sample freezes properly. If your extract is has oils, and I know mint does, the oils can make it hard to freeze. Tricks that can help here - make sure the sample is dilute [yes, it will then take longer to dry, but you will get a better resulting powder], ensure that you have a large surface area - so shell freeze if in a flask, and if the oils are really an issue, add some Teriary Butanol to the water, this will help keep the oily water hating part in solution, and T-BuOH freeze dries really well.