Your program for getting started in backpacking (one night trips close to the trailhead) is excellent. There are a number of skills you need to learn, such as how to stay dry (including not sweating) in cold wet weather, how to pitch a tent in nasty weather, etc. These can be practiced even in your back yard, if you have one! I suspect that in the LA area it will be hard to find inclement weather (except heat!) until next winter. Be sure to do some practice trips in bad weather when it returns to your area!
However, before you buy any more gear, check out the articles in the left-hand column on the home page of this site.
I think you may find that some of what you bought might be heavier than you need. I wouldn't worry about what you already have, but consider this for future purchases. Look at the weights on the gear lists (rather than the brands, some of which are no longer available) as guidelines. Note the slogan at the top of the page: "Packing Light is More Fun." Not only is it more fun, but it saves your joints and ligaments so you can still backpack in your old age, like me! Of course weight is not the only requirement; comfort is equally important, IMHO!
For the wicking underwear, check the athletic departments of big box stores like Target and Walmart. UnderArmor is great stuff!
Water purification--Katadyn Micropur tablets weigh next to nothing, but you'll have to allow several hours for the treatment time, which means carrying more water while it's being treated. If you go to the Make Your Own Gear section and page down close to the bottom, you'll find my thread, "DIY Gravity Water Filter." I never got any pictures posted, sorry, but you can get the ingredients for about $60 and it weighs about 6 1/2 ounces. There's also the Sawyer Squeeze Filter, which quite a few people like and I have not yet tried. You'll have to decide which way you want to go, which will take some trial and error.
It's surprising how few situations really need a knife. I do use a Leatherman--I have very little dexterity with my fingers and badly need the pliers--but I have the Micra, just under 2 oz., which meets all my needs. But if a big herky one is what you want, go for it. If you decide to lighten up later, the big one will still be quite useful around the house and in the car (been there, done that!)
Pants--any synthetic fabric pants will do; nylon track pants (again, in the athletic departments of big box stores) are fine. Right now is a good time to find sales as it's almost the end of track season. I'm not a fan of convertible pants, but a lot of folks like them. They weigh enough more than regular pants, though (it's those zippers on the legs) that you might be better off weight-wise with a pair of long pants and a pair of lightweight nylon swim trunks instead of shorts.
Stove: just a warning--in some places where there are fire danger restrictions, they only allow stoves with shutoff valves, which means you are basically restricted to a canister stove. Check the regulations where you're going to backpack to be sure an alcohol stove is OK. And be really careful with it!
You'll need to decide whether you want to do actual cooking (requiring possibly a set of pots and utensils) or whether you just want to boil water to rehydrate food (requiring only one pot, a spoon and a minimum of dishwashing). I'm a fan of the latter, using mostly home-dehydrated food plus some freeze-dried ingredients bought in bulk. My favorite food site is trailcooking.com
. It has lots of recipes, many using common supermarket ingredients. I'm a big fan of this site and its owner, Sarbar. (You've probably figured out already that I hate washing dishes!)
The gear lists (especially the 7-day gear list) on the home page of this site are good models. Check them against your gear to see what you might be missing. A few things I can think of off the top of my head: some kind of light (headlamp), something to light your stove (Mini-Bic plus matches for backup), lightweight ("liner") gloves and a knit hat for cool nights, first aid items, sunglasses, a sun hat.
For toiletries (you'll at least want sunscreen, some kind of bug repellant and hand sanitizer), take only the amount you need for a trip in tiny bottles. You really don't want to carry a 6 ounce bottle of sunscreen (with the bottle weighing another 2 ounces) for an overnighter when you only need an ounce in a tiny dropper bottle!
I personally am very much in favor of that big tool of the UL backpackers, the spreadsheet with the weights of everything listed (you'll need a postage scale; manufacturers' weights are often way off). Some think this is silly, but I've found mine to be extremely useful. I can compare it against other gear lists to see what I'm missing or, just as important, what I can omit. I can evaluate future purchases by what they do to my pack weight. Even more important, I can print it out as a check list before each trip!