Correct. Delta refers to these as "Basic Economy", "Economy"/"Main Cabin", and "Comfort+". These are all in the main cabin, with a separate cabin for First Class. On planes with a Business Class cabin, Business Class replaces First Class, and a third cabin, "Premium Select", is added between Business Class and the Main Cabin.Basic economy sucks, and sucks more on budget airlines. British Airways is worse than Royal Jordanian. Premium economy is more than the old economy, in that the seats are closer to 1st class seats in terms of space and adjustability, you often get a different meal, etc. I'm playing roulette this time and hoping to upgrade last minute, at least on the flight back. I hate flying cattle car, but will tolerate it for shorter flights. Once you're hitting 10 hours+ I'll spring for the upgrade. Sometimes I get complimentary exit row seats then I'll just stay in coach.
Traveling without bags is best if you can. It really speeds things up when you don't have to wait for the luggage to come out at baggage claim. Plus you can still sight see until your hotel is ready if you get there early and just have a backpack vs a suitcase.
(Note: Delta Premium Select is not much of an upgrade from Comfort+, even on long-haul international flights. A tiny bit more pitch (leg room), the seat reclines a tad bit more, and you get a leg/foot rest, that doesn't really do anything if you're my height (6'2). The food service is exactly the same as Main Cabin.)