Solid wood doors are lovely but expensive so hollow core might be the way to go.  

You must start with how many doors do I need?  Maybe just do the first floor.  There are so many options our there.  Now of course solid wood is everyone's top choice and can be used as an advertising tool when you go to sell and list your home on MLS.  So lets discuss the differences.

Hollow Core: Typically made of honeycomb cardboard encased by fiberboard or veneer shell.  These doors are strictly indoors and are not very solid, they are light-weight but poor sound blockers.  Hollow doors are never fire rated and are best for supplying many doors at a low cost.

Solid Wood:  These doors are individual natural wood elements that fit together to form one unit.  They can be used for indoor or outdoor.  You will find that a solid wood door feels more substantial in your hand and will provide some sound blockage.  The cost of these doors are medium to high.  These doors will maintain their value and give an historical look to your home. 

Now it is purely up to you.  What do you like better?