For XE in a current release you can try 18c.
One problem here is the certification matrix 3 Requirements 18c
Requirement Value
Operating system
Oracle Database XE for Windows x64 is supported on the following operating system versions:
- Windows 7 x64 - Professional, Enterprise, and Ultimate editions
- Windows 8.1 x64 - Pro and Enterprise editions Windows 10 x64 - Pro,
- Enterprise, and Education editions Windows Server 2012 x64 -
- Standard, Datacenter, Essentials, and Foundation editions Windows
- Server 2012 R2 x64 - Standard, Datacenter, Essentials, and Foundation
- editions Windows Server 2016 x64 - Standard, Datacenter, and Essentials editions
Your Windows Server 2019 is not on the list. This does not automatically mean that it won't work but supported it is not. You might get into problems or not. Murphy will show.
It would be best if you can pick one of the supported releases of windows.
Once you got your installation in place, you can use expdp and impdp
to migrate your data. Normally this just works and mostly without
problems.
An other way is to create a database link in your new database that
connects to the old database and use SQL insert statements to pull
over the new data. This is also a valid migration option and
depending on the volume of data it might take more or less time.
My personal favourite way to migrate would be to use database
upgrades. In your case you can not directly upgrade from 10.2.0.1 to
18c. You would need an intermediate version to upgrade from the 10g
version and from that one you can go directly to 18c. From 10.2.0.1 to 11.2.0.4 (event this is not listed as supported) and from there to 18c.
Problem here is you would need an even older windows release to install 11.2.0.4 on..... see Table 2-6 Windows x64 Software Requirements 11g
Given your remark about lack of knowledge I would advice you to opt for the database link since this way you have the least amount of dba skills needed, other than maybe creating the database link. Next advice would be to plan some maintenance and keep up with the oracle releases.