My humble opinion, if you're just getting back into chess and were not playing at a high level before, you don't need a database yet. Fritz is a very good playing and learning tool, and has a large database of it's own.
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The Think Like a King products seem interesting but I don't own them - I can't personally vouch for how good they are. http://www.schoolchess.com/SoftwareHome.asp
If you don't want to spend much, you can normally find a disc of a prior Fritz version at Target for about $10, if you live near one of those stores.
Also, a subscription to this site would do as it has all the features of any chess program you could purchase much more in most cases. I guess a database function to analyze and store games is about the only thing you would need outside of a chess.com subscription and you could possibly make due with the free SCID program if you wanted to go that route. http://scid.sourceforge.net/
I'm getting back into chess after a long absence and am interested in learning about the difference in types of software - i.e. chess database, Fritz, etc. I'm interested in buying chess software to help improve my chess (which needs improvement everywhere). I know how the pieces move, but need to understand the theory of why certain moves should be made. I just watched a video on the Ruy Lopez and was amazed to find out that the knight & bishop moves are made to put pressure on the center pawns. I thought that they were made to put the pieces in a better attack position. So much more to learn than I thought...