You have provided a lot of information for us to make recommendations. There will likely be many. I have just completed a search for a new folder for my 70th birthday. Since I already have 4 folders, I knew what I did not want in a new bike. My budget had a self-imposed limit of less than $2000.

First - craigslist is great if you can look at a bike and assess what it will need to make it road worthy for you and your needs. That's not as easy as it might seem. However, you can test ride and get a good feel for the bike's handling. That's important. Price is often negotiable, too. There's a good chance that you can re-sell on craigslist with no loss. LA is a huge market for cyclists and your selection is probably much greater than most other parts of the county.

Second - A new purchase is, well, a new bike... new chain, new brakes, new tires, etc. The cost will be higher than used, but it's new. To fit your budget you might look at Downtube, Origami, Dahon (from ThorUSA), SoloRock (my final choice), and eBay cheapies.

Third - wheel size - If you are going to do multi-mode commuting you should give serious thought to 16" wheels. The larger 20" wheels make for a larger fold and a heavier bike to lug on/off public transport. The folding time may differ by a few seconds, but more importantly is the chain grease exposure to fellow passengers, the space the bike occupies when folded and the weight of carting up the steps or pushing it between stops.

Fourth - gearing. You mention hilly roadways. Someone else can help there. I live in southwest Florida and the only hills we have are the overpasses. Otherwise, everywhere is delightfully flat and 3 gears are plenty: one for windy days, two for normal riding and three for I feel like a breeze in my face.

Take a look at what's available on craigslist and compare those to new bikes and come back with questions. There are so many knowledgeable folks here that you'll get the best advice available... for free!!