ATC are under no obligation to provide VFR vectors in Class E, and funnily enough in Class E you are under no obligation to follow them even if they did. That's controversial, but you would be foolish not to listen to ATC unless you had a much better reason not to. If you want vectors you can say 'Will Accept Vectors' and they will magically start to arrive. ATC will bend over backwards to make sure you are given what you want, it's not often they say they are too busy, and when they do they will usually apologise and give you another frequency and/or time to try later.
In Class B, C, & D you have to do what you are told. Not all Class D have radar but B and C do, and you will find B and C controllers more likely to use it to move you around. Class D in SOCAL will have radar usually fed off some approach facility. You need to talk to the controller in charge of the C or D airspace before you can enter, talking with center using flight following does not allow you into C or D.
Top tip: if calling up blind just say 'Podunk Approach, N12345, VFR Request' and let them get back, they can be busy and don't want to hear your whole story at once. No problem prodding them every minute if they don't come back.
If you are renting out of somewhere in SOCAL, as part of your checkout get them to take you through all the ATC interactions you will have to make. It's pretty simple stuff, you can also listen to many US based tower/approach frequencies on the Net to get a hang of things.
Weather in Jan/Feb should be great for VFR, but there is some strange wet weather around right now in the SW, bit of a weird winter.
Again, all you need is a Garmin 12XL. A UK one will do fine, lat/long works the same in both places....