Your plan is correct except the outside GFCI should be replaced with a plain outlet, since it will be under the protection of the first GFCI. It needs a "GFCI protected" label to be applied 5 minutes before any inspection.
Generally you should go one of two ways with GFCIs:
Use a GFCI device of any kind in the first location to be protected, and then feed the rest of the circuit downline off of that GFCI devices's LOAD terminals. If you want to make the wiring simple, use a GFCI+breaker instead of a GFCI+receptacle. However, this will reveal any flaw in your wiring, including wiring around a switch.
Use a GFCI+receptacle specifically, in each and every socket location you aim to protect, and do not use the LOAD terminals at all. In fact, the LOAD terminals come with warning tape that says (in as many words) "For Wizards Only - Do Not Remove"; when you wire with this method, you are following the "I am not a wizard" rules.
Most GFCIs let you put two wires on the LINE screws, or you can pigtail.
While the second technique may seem like a waste of money (which it is), it has its applications. One of them is when you want to un-protect a receptacle at the end of the chain. Another is when the downline circuit has a difficult-to-troubleshoot problem, or when it is a shared-neutral circuit.
There are three things you should not do. First, you should not feed a GFCI from the
LOAD terminals of another GFCI -- that is simply playing a "Yo Dawg" joke on yourself, and wasting money.
Second, try to avoid putting a GFCI device past a switch. Some of them do not like having power severed, and will nuisance-trip.
Third, try to avoid putting GFCI devices outdoors. They say they are outdoor rated, but it doesn't really work (partly because outdoor "in-use" boxes don't really work).