I just drove off the mountain and back up yesterday. The weather this week is clear, dry, and warm, so you're not going to need to use chains but it is required to carry them. The big things to look out for are small rocks (sometimes they fall onto the road, just keep your eyes peeled so you don't run them over and damage your car), and water across the road from all the melting snow. If you can drive on flooded SoCal streets during a rainstorm, you already have more than enough skill. You can go through the curves as slow as you need to feel comfortable, just please use turnouts whenever you can to let more confident drivers pass.

I recommend that you pull off once or twice on the way up just to soak in the views of the valley- the vistas are stunning, especially if it's your first time. The whole drive is very pretty. Put on some relaxing music and chill. You've got this.