To move information from a MyHeritage family site, you could:
- Download a GEDCOM directly from MyHeritage
or you could
- use MyHeritage's FamilyTree Builder software (available for Windows or Mac) to sync your family site and bring information down to your desktop. For screenshots see Family Tree Buider: Quick First Look by Tamura Jones.
After you've transferred the information from your online tree to FamilyTree Builder, you can export a GEDCOM file if you want to move the information to a different deskop program for genealogy or upload your GEDCOM to a different site.
The advantage of using the free version of Family Tree Builder is that it will give you a free way to view your information while you are investigating other desktop software that you might like better.
Try different programs to see which ones work for you. I recommend that you choose a family you haven't learned anything about yet to test-drive a program -- choose someone who was a part of the FAN (friend, neighbor, or associate) of your family so you have to really use the program and aren't just slamming the same data into each new program.
We all have different preferences and different research needs. You don't tell us anything about your requirements except that you want a free program. If you are working with names that use diacritical marks, look at the specifications for the software and make sure it supports Unicode. You'll also want to check whether the free version of any software you use will accept a tree that big, since some free versions limit the amount of people you can have in your tree. We can recommend software based on technical requirements, but we can't know what you like or don't like in a user interface, so try free versions out and see what suits you best.
What data might be lost in the transfer?
Tech-minded readers can find an extensive feature comparison by Keith Riggle on the website Genealogy Tools, in the article Family Tree Maker to GEDCOM to Other Apps Crosswalk (Updated 26 Oct 2019), part of a series Riggle wrote after Ancestry dropped support for their software Family Tree Maker.
But what about paid software?
Disclaimer: I use and recommend Family Historian as my main software, which is not free. Family Historian has an enthusiastic and knowledgeable user group, and shares knowledge via their forum and Knowledge Base. I tried several different programs before choosing it, and it was the best fit for my own needs. There are several articles about transferring data from other programs to Family Historian in the FHUG Knowledge base that might be useful to you, even if you don't choose Family Historian for your software.
It's smart to "kick the tires" via free versions or trial versions before making a final decision, but if you rule out all the paid programs forever, you may miss out on powerful tools that could help with your research.