Having dealt with Medi-cal for someone else in the recent past, some warnings for you:
You're not going to get to pick your doctor. Theoretically you can, but since so very few actually accept Medi-cal patients, you're hog-tied. When my daughter had to be on Medi-cal for a while, I phoned literally every doctor's office within 20 miles that was listed in our phone book (and that was a lot of calls) and found none that would take a new Medi-cal patient. Some won't even take you on at all as a self-pay if you don't have private insurance.
You will be sent a list of "providers" once your application is approved. You will then need to contact each of them to see if they are taking new patients. Assuming that your situation is like ours was (in a major metro area) you will then need to contact Medi-cal and tell them you can't find anyone. You will be assigned to a clinic/doctor, which may or may not be anywhere near where you live, but which will be in the same county. Typically, these will be in areas of extreme poverty. The waiting lists are extensive.
If you have a medical emergency you can go to the emergency room, where you will be seen and stabilized. They may ask you for a deposit to cover further care - if you really should be in hospital or need medication - if they know you have applied for Medi-cal and do not have insurance and are in a poverty situation. If you cannot pay it at the time you are in the ER, they may ask you to sign a contract for later payment.
The formulary for Medi-cal is limited - your doctor may think a particular med would be good for you, but it may not be available on the formulary. You can still get an actual prescription for it, but if it's not on the approved drugs list you will have to cover the cost. Be prepared for sticker shock if you are paying out of pocket for medications in the USA. (A course of an antibiotic for a sinus infection, for example, can go into the three digits if it's not Amoxycillin in the generic form.)
If you have much in the way of resources at all, you will probably not be able to get on the Medi-cal roster. This includes your automobile, if it is newer/worth more than a certain value. Your employment status will be considered, but so will any savings or property you may own. Persons under 18 have a very much less rigorous application process, and your child may also be able to get dental care until they turn 18.
You may want to look at the Covered California website and see if you have any other options at all. I think it is designed for employed people, and I haven't looked at it in a year, but perhaps you might get lucky and find a policy you can purchase out-of-pocket there. Almost anything you do find there will be better than Medi-cal. Kaiser HMO is a decent option. You might also check joining Kaiser outside of Medi-cal, if you can.
My daughter used to occasionally work in various medical offices affiliated with a publicly-funded hospital in California. Several times she worked in the insurance sections. She would come home very sad some days, saying she'd had conversations with patients she knew were going to die because they were in Medi-cal and not a private insurance like Blue Cross, because although treatments/medicine was available, they were not going to get it. If they'd had private insurance, they would have. She had to tell them that their treatment wasn't covered.
My advice for you, in the meantime, is that if you become ill enough to need medication, there are "Minute Clinics" in a lot of pharmacies now, where you can pay between $50 and $100 for an appointment and get a prescription, if needed. You will, of course, then have to pay out of pocket for the prescription as well. But combined they may be well under the cost of an actual doctor's office visit. And, again, if it's an emergency, go to the emergency room. They have to treat you until you are stable - and then they can dump you in skid row in your hospital gown if you can't pay. If you do rack up a big bill with them, if you do finally get Medic-cal, there may be a provision to cover retroactively charges for "catastrophic care".
You'll be happier once you are here and on the NHS. Be happy you have the option to be on the NHS at the minimal charge the government lays on you.
Best of luck with it all.