For Python/ArcPy, I would look thru some of the thread that have suggestions. There are many choices.
ArcGIS 2: Essential Workflows (10.4) Class Resources (has links from that class)
/blogs/dan_patterson/2016/05/09/the-links Lots of resources, some may be more advanced.
To get a feel for GIS (esri)
Esri Video | Videos Covering GIS Events, Products, People, & Topics many topics from beginning to specific topics (free)
https://www.esri.com/training/#!/ (some free or low cost training options...also more in-depth options)
For low cost personal-use access to the software
or you can usually get a ArcGIS Platform | Free Trial version to just test it out.
There are some free classes that us the ArcGIS Online as the platform that run about 4-weeks (called MOOCs)
These are just a few of the "learn-on-your-own" options....but don't count out a local school that may offer classes too.