I don't think it matters very much. If using methanol or a water miscible solvent, the water will just go into that solvent. If using a water immiscible solvent, the compounds may partition in the small amount of water, but such compounds aren't likely to be soluble in your extraction solvent anyway.

I assume that you mean water with the term "moisture". If so, a polar solvent such as MeOH, EtOH, acetone will step by step extract the aqueous moisture from the material thereby extracting the compounds which are soluble in the solvent used for extraction. If you extract with an apolar solvent, extraction time should be longer because the apolar solvent has to dissolve the aqueous moisture in small amounts which will take time. If you don't, there will be aqueous sectors, which the apolar solvent cannot pass and from which the compounds to be extracted are less extractable. You should also be aware that in moist material degradation of the original compounds can occur.Thus a well dried material should be the choice in any case. 

This is a general answer to your question. Plants in general are stored after drying them to a constant moisture content in an oven (60-70oC for 48-72 hours) (for nutrient analysis). In case they are Sun or shade dried (for phytochemical analysis), the moisture content should be around 8-10% to avoid fungal and other pests contamination. Plant biomass powders stored in tightly capped glass or plastic containers and stored under ambient or under cold storage retain their characteristics up to 6 months. Medicinal plants are mostly dried in Sun or shade before storing or marketing.

Check this thread for some informative posts:

https://www.researchgate.net/post/Which_do_you_recommend_fresh_or_semi-dry_or_dry_biomass_tissue_for_an_aqueous_solvent_extract_or_for_extracting_isolating_separating_phytochemicals

It should not be more than 50% of the total soluble content of the plant material.

Yes, it should not be more than 50% of the total soluble content of plant material. Thanks.

You have to grind your sample for soxhlet extraction therefore I think you shouldn't have more than 20%, and in my experience it's better if you have 10%.