Hi, fellow Chicagoan!
I've flown into LAX and rented a car twice. I had no problems with it, but it it a longer trip, and if there was traffic it could be way longer. That was the main problem with it. Big airports don't really bother me (since I'm used to Chicago

), and LAX does offer more direct flights.
On my recent trip I flew into Orange County/John Wayne. It was very close to DL, which was a huge plus. However, a warning to you and anyone else on the transportation from the airport. I took a shuttle, and I didn't book one ahead of time because you didn't need to and I didn't want to be locked in. So I got there (my suitcase was missing, due to a close connection because of weather, so I was already in a bad mood) and found a guy in a Super Shuttle shirt. That was the shuttle I was planning to take, because I'd used them before in another city. I asked him for a shuttle to my hotel, and a waved a van over. It wasn't Super Shuttle, but he said it didn't matter, it was the same price ($10). So I got in and the driver said we would leave in 10 minutes. So I waited a couple of minutes, and then I called my mom. I talked to her for a while, and then another woman came and got in the van. He told her 8 minutes, but I had already been waiting for well over two minutes. Okaaaay. So I told him that it had already been more than 2 minutes, and he said no it hadn't. Then another couple came and got in, and he told them however many minutes it would be. I looked at my phone and I had called my mom 12 minutes ago, so I had already been waiting for 14 minutes, so I told him so. He said, no it hasn't been 10 minutes yet. His supervisor got involved and they were telling me that they write down the time when someone gets in and it hadn't been 10 minutes yet, but I knew it had been. So then they were like, you can get a cab for $40 if you want to. What do you want for $10? They were horrible. I wouldn't have minded it as much if they would have said we want to hold the van for a few minutes to see if extra people show up. But when they're just
lying to me and telling me I'm wrong, and insulting and threatening me (they were acting like they were just going to throw me out), that was just outrageous. So I shut my mouth (with the occasional grumble

), and waited until we left, and got to DL too late to see the DEP that night.
So I would be wary of getting a shuttle from that airport.
Going back to the airport, I called Super Shuttle the day before, and I had no problems with them. They were actually a few minutes early, but it produced no real problem. The driver was very nice. What a change from the arrival.
One other tip is that the security line at John Wayne was loooong. It wasn't a big deal for me, because I was there plenty early, but a lot of people were worried about missing their flights. They only had one line, and I think two conveyers, so it took a while. So show up early if you go through there.
And have fun! I love DL!