My route (I've included my IGT splits, as seen in the Free Mission mission select, though some of them—especially towards the beginning—aren't optimal as my PR run had a bit of a slower start):

M01 "Shorebirds" (5:17) - Shoot down two waves, but be sure the eighth plane goes down just after the in-game clock reaches 5:30. If it's before that, the third wave will spawn. You CAN shoot down all three waves, but it's harder than just being a bit more patient. M02 "Open War" (3:11) - Not much to say here. M03 "Narrow Margin" (6:13) - In the second phase, prioritize the ships. M04 "First Flight" (4:44) - You can actually start shooting the third wave of bombers before they appear on radar. They'll always appear behind Lt. Col. Ford.

Thanks to weirdozzie's run, I became aware that the F/A-22A Raptor is available earlier than the wiki documents. Here, after the Rendezvous briefing, quit to the title, enter the first mission of arcade mode, then immediately exit back to campaign mode and buy the Raptor.

M05 "Rendezvous" (7:47) - F/A-22A M06 "White Bird Part I" (8:58) - same as M05 M07 "Front Line" (7:17) - Buy the F/A-18C. Phase 2 (where the Scinfaxi fires missles) activates when eight ships have been destroyed. Save LASMs for the Scinfaxi. You should be able to take it out in one pass. M08 "Handful of Hope" (7:55) - F/A-22A. Fly straight from the start until you reach the first big circle. From there, make sure the transport is close enough, then fly due north at full speed, aiming for a narrow gap between bubbles. The transport plane will got shot at once, which is fine. M09 "Lit Fuse" (11:47) - F/A-18C. M10 "Blind Spot" (3:27) - F/A-22A. The transports and the jammers can be taken out with 2xXMAA, and you can actually machine gun the jammers before Grimm points them out. M11A "Chain Reaction" (4:19) - same as M10. You DEFINITELY want the A missions here. M12A "Powder Keg" (1:39) - F-5E. This is why you want the A branch: you can just bomb the tunnels and not worry about lining up your approach at all. M13 "Demons of Razgriz" (2:32) - F/A-18C. Use its LASMs on the Hrimfaxi after it resurfaces. You should be able to take it out in one pass. M14 "Ice Cage" (7:27) - F/A-22A M15 "White Noise" (5:20) - F/A-22A M16 - Either branch works here. Personally, I prefer the A branch since I don't have to switch planes. 16A "Desert Arrow" (15:43) - F/A-22A 16B "Desert Lightning" - F/A-18C Either way, save your special weapons for the mission update. M17 "Journey Home" (11:38) - F/A-22A. When the F-117A spawn in, prioritize shooting them down since they're the trigger behind phase 3 activating. M18 "Fortress" (7:05) - F/A-18C M18+ "8492" (1:51) - same as M18. Fly close to the altitude cap to maximize your speed, but make sure you're low enough to trigger the 8492nd's dialogue when you pass them. M19 "Final Option" (8:31, but I didn't get the skip. A good time here is around 7:15) - Hawk [unarmed]. There's a trick to save about 1:45. I'll have a video linked below. M20 "Ancient Walls" (11:52) - F/A-18C or F-14A. It depends whether you want LASM or SAAM. I also just don't like the Tomcat, so I use the F/A-18C. M21 "Solitaire" (3:13) - I use the F/A-18C because I also use it in M20 and M22 and it's easier not to change, but the Raptor might not be a bad choice either. M22 "Closure" (2:13) - F/A-18C. Just spam everything at the rock bed and you should be able to take it out in one pass. M23 "Ghosts of Razgriz" (5:39) - F/A-22A. I fly around the map counterclockwise, and fly over the canyon to connect with the targets I've missed. The trick to a good time, though, is getting a quick fight against Grabacr. M24 "White Bird Part II" (5:54) - F/A-22A. Focus on those engines. M25 "Heartbreak One" (11:13) - F/A-22A. This should go without saying, but take the shortcuts. M26 "Sea of Chaos" (5:10) - F/A-18C | F-14A. Again, it depends whether you want LASM or SAAM. I use the F/A-18C. M27 "Aces" (7:31) - F/A-22A M27+ "The Unsung War" (5:38) - same as M27. You can fly in the back side of the SOLG (it's hollow). Destroy the center with machine guns and wait for the screen to fade.

Final Option (M19) Skip: Video (daapdary on YouTube):

Play the beginning of the mission as you would in any other playthrough. Once you get to the first cave, slow down enough that Pops says "Stay close to me. You're straggling." while you're in the entrance of the cave. This isn't an extremely tight window, so you don't have to be terribly precise, but earlier in the cave is better than later. Then hit the afterburners and fly towards the final cave as quickly as possible. Then race through it. Saving time in this mission is all about flying through this second cave quickly.

Other notes:

¤ Your wingmen are very unreliable. Definitely expect to do your own fighting. Anything they do is bonus, though they can also come in clutch from time to time.

¤ If you're struggling to shoot down a particular plane (esp. Grabacr and Ofnir), try targeting a different one. You'll probably generate a better angle, and they'll be less likely to evade. Head-on attacks are particularly useful.

¤ I'm not sure how useful this is in general, but you can fly near the altitude cap (about 32 000 feet) to fly much faster than normal. With the MiG-31, flying at a level 6407 feet gives a top speed of just under 1500 mph; stalling through the altitude cap gives a top speed of just under 1900 mph.