If your original vinyl floor was installed using a full spread adhesive method, then you can apply an embossing leveler to the original vinyl to smooth it out and then install the new vinyl.
Hardwood flooring expands and contracts due to changes in temperature and relative humidity. Having adequate levels of humidity in the home will help minimize the shrinkage of your floors during the heating months.
Solid hardwood should not be installed below grade. However, engineered hardwood can be installed in basements as long as you do not have an existing moisture problem.