The choice of DAW software is going to come down to choosing from the market leaders. These are the brands that, through having a good reputation, have become the most widely used in the recording industry.
There is freeware out there but, you will find out that you will outgrow them very quickly. One of the most well known is Audacity, By all means, have a look but, for a home studio, I would recommend purchasing one of the leading brands.
These brands tend to offer different versions of their software with some of the functions limited. These versions tend to be cheaper than the full versions. So, this may help if you are on a limited budget. Additionally, look out for bundles as many studio equipment suppliers bundle together DAW software and audio interfaces.
Here are six of the top DAW software products: