You can get a personal use license to learn skills and build your portfolio: https://www.esri.com/en-us/arcgis/products/arcgis-for-personal-use/buy
There are many tutorials on the Documentation gallery. I recommend starting with this series for beginners: Essential ArcGIS Online skills, and branching out from there. If you start with ArcGIS Online skills, you won't have to invest in a fancy computer right away.
After you've completed some tutorials, go to Esri training, where you can find more courses, including MOOCs and instructor led classes. They also offer certification. This is probably a good route to take if you are not going to enroll in a university, since it can provide proof of your GIS skills on a resume.
You might also find a mentor in the industry. For example, there is a mentorship program offered by URISA.