Unless you really go nuts and spend 10 hours per day in the park, reality is that you're going to miss something "big" if this is your first trip to WDW. And like others here said, I definitely would not recommend trying that. WDW is huge. If you've never been, you can't really comprehend its' size and how much walking there is...even for an experienced veteran who knows how to get around, it's a lot of walking. Being new to the parks, it's almost unavoidable that you'll criss cross the parks at least once, simply because you're learning the layout of the land. Nothing wrong with that, it happens. Full rest days are up to you, only you can decide if you want to do that. I'm not a fan of them personally, but I totally understand why people do them. For us, a "rest day" is 3 or 4 hours in the park, then back to our rental to hang out and relax. But no harm at all in taking a day to hang out at the pool and chill...and take a nap...or three.
Best advice I can give is to "stop and smell the roses". Since you won't see "everything" anyway, take the time to enjoy what you do see. Use the online maps to see what is in each park. Ask questions here about specific rides, or use YouTube if you'd like. Figure out which ones you want to ride. Work them into your FP+ plans if they're popular rides (folks here can help you with that too). But I'd recommend having flexibility. If you plan to ride Rock n Roller Coaster (if you like thrill rides, I HIGHLY recommend it) and you want to stop and look around the gift shop or look around the shops you'll pass on your way too/from, then do it. Take the time to soak in the atmosphere and your surroundings. Don't have your plans so packed that you run right past all kinds of things you may have been interested to see (but didn't know existed) simply because you have a tight deadline to make.
Getting to the parks early is a good idea. I don't like doing "rope drop" where you show up 30-60 minutes before the park opens, but we'll show up right around opening time. You can get a lot done in that first hour the park is open. Alternatively, have a day where you sleep in as long as you want, have a relaxing breakfast and/or lunch and get to the parks later. The last hour the park is open is also a great time to get on rides, the lines go down significantly.
As for what rides are "must do". Uhhh...for me, it's pretty much all of them.
Each park has some thrill rides, plus lots of other stuff. For a quick list of thrill rides, I'd say RnR, Space Mountain, Big Thunder, Dinosaur, Expedition Everest, Tower of Terror, Splash Mountain (not a "thrill" ride since it's on the water, but thrilling enough). I know I'm leaving some out, but that's just a off the top of my head list.