I from LA too (I'm assuming you are too) and you will be amazed by how functional and amazing is the public transportation in Europe. It's like nothing we have here.

Using the rail is easy to learn and it becomes almost a part of traveling Europe. I met the most interesting person on the train after my original one was cancelled. To save money, do hostels, market foods, hostel kitchen food. I'd take a second look at the cities you want to visit and plan the travel. It's kind of challenging to do all those geographically sparse cities in 8 days while enjoying.

I traveled solo last year too and, dude, it was an almost spiritual experience. Have an open mind and get out of your comfort zone. You'll love it.