Thanks for the tips and the insight, guys. Yeah, I've rented a zillion cars over the years and car rental companies are certainly more alike than different. As a general (but by no means absolute) rule, I think you're more likely to get a newer and better equipped car from the "major" companies. You're also slightly more likely to get a faster pick-up and return. I also think you're slightly less likely to be hassled to upgrade and for insurance. For these reasons -- and the fact that you can usually use codes and coupons to make the big boys' prices the same as the smaller competitors -- I usually stick to the majors. Oh, and the "fast rent" cards sometimes save a little time. But I'm not going to find a major willing to give me a minivan for $125/week.
I'm glad Thrifty's location is convenient. I think I have used them before at LAX, but it was like a decade ago, so my memory is very hazy.
As far as hotel parking goes, I have also USUALLY been able to park on the street at the LAX hotels, but not always. I usually priceline my LAX hotels, so I'm never sure which one I'll get. Last year, I got the Radisson, which is the closest to the airport (easy stroll to Terminal 1), but didn't have any obvious on-street parking. Since I was flying out the next morning, I returned the car and walked to my flight.