All basement flooring ideas must take into account the tendancy for basements to be cool, dark, and damp. Basement moisture is always a threat as it seeps in from below basment floors and does all sorts of damage.
Your main choices for a basement floor are a hardwood floor, concrete, carpet, a laminate floor, an engineeered hardwood floor, and a porcelain tile cement. Carpet and hardwood basement floors may not be the best options because of the dampness issues.
Installing an engineered basement floor might be a good alternative to a hardwood floor if you like that kind of floor. They usually have a higher resiliency to any humidity changes that allow it stay dryer than many of your other basement flooring ideas.
A laminate basement floor can be constructed from moisture resistant materials and they can be "floating" floors which are not directly attached to the floor beneath it. Most laminate is OK but some is not so you need to check with the manufacturer to make sure the laminate you choose will work for basement flooring.
The most popular and perhaps easiest basement flooring ideas is to just paint your cement floor. You can be careful to choose the right basement colors for your floor so that it creates the atmosphere you desire. Painting your basement cement floor is the safest option because you are not investing a lot of money on the floor only to find out later that it has been damaged due to basement moisture problems.