There are many types of tiles to choose from that provide a high slip coefficient. Keep in mind, the higher the slip coefficient, the more difficult the tile is to clean. Most tiles today offer a nice balance between ease of maintenance and safety.
Laminate floors are not attached to the subfloor. They float above on top of a dense cushion. As a result, they do have give when you walk on them.
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.