Are you staying near Hollywood first, or staying near DL the whole time?
Burbank isn't usually recommended because traffic's awful. Well, it's awful everywhere, but I understand Burbank is especially bad.
There's four others: SNA (Orange County, aka John Wayne); LGB, Long Beach; ONT, Ontario; and LAX.
For DL, SNA (12 miles from DL) is the most convenient, but it is also usually the most expensive to fly into. LGB (15 miles) and LAX (35 miles) are cheapest, but more expensive for shuttles, etc. That won't matter if you're renting a car. Ontario (35 miles) is small and sometimes less expensive, but far away.
If cost doesn't matter, go SNA. If it does, check to see which is cheapest. LGB gets a lot of votes around here.