I can't think about anything that you should avoid. Just don't spend too much time in Tijuana. Is not bad but is not the most charismatic town in Mexico.
For me the real Baja starts once you pass El Rosario. That's where you make the turn east and where the really scenic Baja is. That's also the longest stretch (El Rosario to Guerrero Negro about 210 miles) with no gas stations. most of the time there's somebody selling gas in Catavina on the side of the road which is half way between those two points.
You can get the required insurance from any place in San Ysidro and cross there. As soon as you pass the Mexican Customs you'll see the sign that says Rosarito Cuota, get in there and that's it. that's the toll road that will take you to Ensenada and from there you can't get lost.
In regards to the route I would recommend to stay on the main road (Hwy 1) and take side trips from there.
Santa Rosalia is the ugliest town in Baja but is also the beginning of the best of the trip. I really like Mulege and Loreto after that.
If you want some dirt on the way back North, once you pass Guerrero Negro, you can take the gravel road to the right from Chapala that takes you to Puertecitos and San Felipe. That's about 50 miles of dirt and about 80 of pavement to San Felipe. From San Felipe take HWY 3 back to Ensenada.
You probably know this already but you don't need a importation permit for the vehicle to ride in Baja but you will need it for the rest of Mexico.
You will find several military checkpoints but they will only ask you to open your side cases, take a look and away you go.
I've been in Baja several times in car and motorcycle and never had an incident.
If you need a place for your trailer I live in Escondido and I have plenty of space in my front yard. It's fenced all around.
Good luck and if there's anything I can help you with let me know.