For the Bay Area and PHX, you will probably end up flying Southwest, if only because they have the most flights. Southwest also has one-stop service to FLL.

If you accumulate 32 flights over 12 months Southwest gives you A-list status, meaning that they automatically check you in and you board early, and you also get priority for security screening. If you have use for their Companion Pass (free travel for a specific person when you fly), then you need to figure out how to reach 100 credits within a year. Regardless, if you end up flying on Southwest at all you should read the FAQ.

Today's Southwest sequential boarding system is nothing at all like the horrible mess it was 10 years ago. IMHO, it's the best boarding system in the industry. I can sit down until the right time, then be handing over my boarding pass at the scanner less than 60 seconds later. I control the probability of an empty middle seat by selecting my row, so I have more room than I'd have short of an upgrade to F on any other airline.

There's a free shuttle bus from the Green Line metro station to LAX. You can also take public buses to the airport if you are close enough for that to be practical.