It's no fun dragging a boat thru downtown LA, but if you can live with that, Marina Del Rey is an excellent launching point. It has lots of secure, inexpensive car/trailer parking. It has good ramps. It has guest slips at the end of Burton W. Chace Park for $0.50 a night. It's not the commercial shipping hell of Long Beach. And it's almost due north of Catalina.
We arrived in early afternoon, set up and launched the boat, and found an open guest slip. Had dinner with friends, did some last-minute shopping at West Marine & a grocery store (both a stone's toss from the launching area). Then we spent the night in the slip and left at first light.
You exit MDR, gain about 3 miles offing (by motor, if needed -- wind doesn't fill until about 10 AM), and point your bow 180 degrees true. Congratulations: hold that heading on a close reach for 8-10 hours, you hit the Isthmus. You have a 1kt current at your back. It's ~32 NM to Two Harbors, which is a better place to aim for than Avalon, especially in peak season. Avalon fills up early, and its overflow is Desconso Bay -- the nastiest, rollyest moorings at Catalina. Fun place to visit -- wouldn't want to moor there.
Two Harbors has overflow moorings on all sides, and even beaches you could pull up onto. You could also aim for Cat Harbor, tho we were too nervous to try that first thing. Next time, I think we'll go straight there from MDR & anchor in the shallows. Two Harbors has a stringline, which is a series of closely-spaced small boat tie-ups right near the beach. There is always room to squeeze in another boat your size. Stringline spaces are inexpensive and you can practically wade to shore, but they are also noisy on weekends. And when the wind is from the W to SW, you may be surprised to exit the calm lee of the island to find the wind screaming at 20kts straight out the Isthmus and down the fairway. Our little motor couldn't make headway, and we were forced to ask for assistance from the Harbor Patrol (which is much mellower than Avalon's). In our defence, that same wind forced the MDR ferry to make
three attempts before catching the dock.

Assistance is free if you are inside the green buoy near Ship Rock.
From 2H, you can scoot down to Avalon pretty quickly. Getting there early, preferably early in the week, will help you snag a mooring. You will need to go a couple miles offshore to catch decent winds. If all the spaces are taken, wheedle Harbor Patrol for a mooring right behind the Casino mole. There are a number of shoreboat tie-ups there they can rent if their owners are amenable. The HP felt sorry for our small boat and stuck us there, rather than Desconso. It's v.protected from the swell but catches lots of boat wakes.
The trip back to 2H from Avalon was wind right on the nose and 4-foot swells. But since it was only 10 miles and we had nowhere to be especially, it was also the best single sailing day of my life.

10-12 knots true wind and the boat was running like a greyhound. We did it in 5 tacks, laughing our heads off.
Evey sailboat we saw making the same trip, in either direction, was motoring.
The trip back to MDR is not quite the sled ride to Long Beach. You will have a current in your face and may want to get inshore sooner, then head up the coast. But the wind should be a beam to deep reach and you will simply fly home. Entering MDR in late afternoon was harrowing for us: we aren't accustomed to that level of boat traffic, and the waves are breaking as you try to tuck in behind the breakwater. Once inside, observe the traffic schemes and you will be fine. We sailed right up to the launch ramps.
IIRC, you
officially need permission from the LA County Beach&Rec people to park at MDR more than 5 days. They told us, Come, park, stick the right number of vouchers on your windshield and you'll be fine. We bought one extra, just in case we wanted to spend another day or the weather was bad.
We bought the video
Cast Off for Catalina, which is a little cheesy but really helped us sort out the various harbors and protocols.
My only other advice is: Go. Go now. Have fun, try to miss the big metal boats, and let us know how it went when you get back. Cheers!