Your question could take many paragraphs to answer thoroughly.
Here's a quick recap. Maybe someone else can elaborate more.
The 737 does mostly domestic flying with a bit of Mexico, Caribbean.
Mostly 3 or 4 day trips with quite a bit of longer range stuff. Transcons to NYC, Boston, Florida, etc. plus west coast to the eastern hubs, (DTW, MSP, ATL,). etc
The 757,767 is a mix of domestic and international. The 757 flying is very similar to the 737. The 767 flying is a bit of Europe (mostly Paris next month) and a lot of Asia and Hawaii. You have trips as long as 10 days that go in and out of Tokyo, Nagoya, Guam, Beijing, Shanghai, Honolulu, etc. etc. Lots of layover time in Narita.
The reserve rules are hard to explain in a short forum post but the basics are that you are on call about 16 or 18 days each month. You have some (up to 6) days on "short call" where you have to be at the airport in 2 hours or less after the phone rings. The rest of the days are "long call" and you have 12 hours to make it in after contact. You basically have to live local or have a crash pad. Bottom line = Commuting to reserve sucks. If you live in base its not so bad except the pay guarantee needs to be higher. (its only 70 hours)
How long til you can get based in LAX is the hardest question. It depends on how much hiring takes place after you get hired. No new hires have gone directly to LAX but it probably won't be long til they can get there if upward movement continues. The bottom reserves in LAX are pretty junior on both the 737 and the 7ER. However, if the economy slows, things stagnate and hiring stops it could take a long time. Nobody can predict for sure.