There's a disease called peach leaf curl. The link (below) is the UC Davis low-down on controlling it.

Make absolutely sure you get a low-chill variety, because LA doesn't have enough chill for many cultivars.

Mulch, yes, with composted material, not gravel or rubber or the stuff that is uncomposted dyed wood. Keep the mulch away from the immediate base of the tree (to prevent rot). Renew it when it gets thin.

Fertilizer--if your soil is anywhere near decent, you won't need much. Mulch, as it breaks down, provides trace minerals that the tree needs long term. Light applications of nitrogen-high fertilizer, once in early spring, once in late spring will provide a good leaf canopy, however, if you overdo it on the nitrogen you get a massive leaf canopy and this encourages pests and diseases.

The main things are: peach leaf curl control, and choosing the right cultivar. It also helps to have flowers such as alyssum and lavender nearby year round. Why? to encourage bee visits so they pollinate your peach flowers.

Don't fill the planting hole with planting mix. Plant the tree in the native soil and place mulch on top of the soil--earthworms will pull the decaying mulch down into the soil, process it into something the plant roots can use. Woody material below ground encourages root rot and robs the soil of oxygen, which the plant roots need. Don't plant the tree too deeply. The flare at the base of the trunk should not be covered.

Well, that's about all I can think of.

Here is a link that might be useful: uc davis peach leaf curl notes

there is also a very active fruit forum ... when you run into problems

ken