I also live in Southern California, so maybe I can help you out some.
Definately go with the 20L to start out with - you won't need to replace it for a few years, at least not until your snake starts to crack 3 feet. Like Rita said, a 10 gallon really isn't big enough to give a proper heat gradient between cool and hot.
I recommend going with an undertank heater and an overhead light. Do you have AC in your house? If you don't, don't worry a whole lot about heating until the temps drop to about 70 or 80 during the day. If you do, it probably drops temperatures to in the 70s during summer, is my guess. Use the overhead light at a low wattage (I have a 55 gallon and I use a 75 watt bulb for summer) to up the heat to the low to mid 80s, and then mount the undertank heater on the side of the tank (that's actually the method the manufacturer prefers) to make one side of the tank in the high 80's, low 90's. In winter, just up the wattage of the bulb (I go up to 125, but living on a mountain means freezing cold winters), and things should stay in the right temp range. I put both the light and the heatpad on the same side of the tank, with thermometers at both ends.
I like to use a thermometer that has a probe that goes into the tank and a digital readout for outside, because it gives a much better idea of the air temperature than the strips, which are pretty much giving you the temperature of the glass.
For your baby, papertowel works best until you're familiar with what normal poops are, how often it poops, and the sort of messes it makes. Seems like a wierd thing to know about, but if you know what a normal poop should be, then you also will know if the snake is making abnormal poops, or if it's not pooping when it should.
Once you're familiar with that, then you can use something a bit prettier than paper towel. I like mixing dry forest bedding (or ecoearth) with reptibark. Bark is just easy to clean, and with the forest bedding inbetween there isn't gaps to the glass underneath. Aspen bedding also works, but I've had people come into work and complain about getting mites more often when they use it. It might be just a socal thing, or just my area, because I've noticed big breeders or even small breeders in the east using it and not complaining.
Water dish - just make sure it's big enough for it to soak in, small enough for it not to drown. I use a dog dish for mine, since they're a bit large for most fake rock bowls you find in pet stores.
Hidey - I use a shoebox with a hole cut out. When it gets dirty or too destroyed, I just toss it out. Since the baby will grow quite a bit, something similar to the shoebox probably would work best until it's gotten to be full size, because hidies can get pretty expensive.
Cage "furniture" - Having a rough surface in there is extremely important for good sheds, and a thick branch that'll support the snake's weight is good for climbing and exercise. Manzanita or grape branches work very well.
Humidity - Not a big deal when you're using bark or forest bedding. Just mist it once or twice a week and that'll keep it damp enough for the snakes but not so damp that they'll get sick. Usually having a good large waterbowl near the heat sources (but not under them) keeps the humidity up high enough.
I hope that extremely long post helps! 
~jenny
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1.1 normal ball pythons (Cindy and Darwin)
1.0 rex rat (Scurvy)
0.1 bunny (Spazz)
2.1 betta fishes (Vicious, Killer, and Butters)
3.1 great danes (Shasta, Odysseus, Merlot, and Watson)
1.0 fat fuzzy mutt (Smokey)
1.1 cats (Thidwick and Turtle)
2.0 horses (Buddy and Sam)
1.0 goat (Billy Jack)
2.25 chickens (Jacques the rooster and his harem)
but what I really want is more ball pythons!