I've just started playing with Fusion 360 myself, having seen it recommended by a few of the guys here. To say I'm impressed is a huge understatement. I generally use Rhino, AutoCAD or Sketchup when designing (mostly furniture, props and museum interactives) and I've been aiming to use Solidworks more. Fusion seems more like Solidworks than any of the others, but doesn't cost zillions of pounds. I'm really looking forward to getting my teeth into it.
I'm mainly replying here to see if you've checked out any Makerspaces? For those of us living in tiny shared flats with no shed/yard/garden etc. they can be invaluable places to use shared machinery that would otherwise be inaccessible, meet like minded people and even do courses in things like CAD and CAM (courses that are often free).
There's a brilliant one near me in Hackney that has a shared workshop equipped with lots of kit including lathes, mills, a laser cutter and a small CNC. I'm sure there's probably even more in LA - like this one: http://hexlabmakerspace.com/
(I know LA is a big place, but if you search maybe there'll be a Makerspace near to you. They're normally very friendly places, with lots of people itching to help fellow makers)