mjhjmtu

Is Blender 2.8 different enough that I should wait for the beta to be released (in a couple weeks?) to start learning the software, or is 2.7 a worthwhile starting place?

Learn now, and it's ok to start with 2.8

Blender 2.8 makes many changes to some fundamental aspects of how we interact with the software and with each workflow. Most notably: layers are gone and the objects are organised differently; using workspaces for different kind of tasks is now visually encouraged (with some great default workspaces!); the creation of materials is done with a new efficient LookDev mode.

Many shortcuts were changed, included commonly used ones; almost all the icons are changed too, and the interaction with the Viewport has been improved in many ways.

Since it appears that the Alpha 2 version is stable for most of the users, I'd suggest trying Blender 2.8 directly. You won't have the burden to re-learn new shortcuts and to get used to new defaults.

Just don't rely on an experimental version for anything professional, but as I understand you are just trying to pick up a new hobby/interest, and Blender 2.8 won't hurt you! Some tutorial creators have already started publishing 2.8-based videos (but 2.79 tutorials will be mostly fine too, with some effort to figure out the hotkey changes)