Well, I'm not into TFIV right now, but give me some time and I can supply more vital info.
Those last weeks were almost TFIV exclusives. My route was Strite>Daser>Ruin>Air-Raid. Here's my reasoning:
Strite -- In this stage the boss takes a long foreplay, which just drags too long. Having it done first makes for a less boring play later on. Having the toughest boss (Gargoyle Diver) out of all four prologue stages defeated so early on is another asset.
Daser -- Probably the toughest stage, because of those silver ships coming at you fast, front and back, some firing long red laser shots, which are hard to avoid. Here I get my first Shield-item. Whenever I failed here, I did a reset, but since it's my second stage, the time waste is small.
Ruin -- Considerably easy and fast, cause of the constant slow-downs and its short boss fights respectively. Usually my shield is used up to red from the Daser challenge, but it's not required to have one here anyway.
Air-Raid -- Another tough stage, but with the Hunter weapon you get in Ruin, it becomes easier and so much more fun. It's a varied and exciting stage, so you won't get bored, thus won't make mistakes caused by inattention.
Brief impressions of the later stages:
Stages 6 (Volbados) & 7 (Desvio) are really easy, the latter features my favorite boss by the way (Dust Eag), and I always took the upper route. Now Stage 8 (Bio-Lab) is different, because of its boss rush structure, and is also a key stage, i.e. your performance here will determine your performance during the rest of the game. As with stages 6 & 7, I only tried the upper route.
The hardest part is to survive the second mid-boss. Why? Those waste ejecting tubes on the ceiling are very annoying, add the long, precisely aimed laser shots of the mecha on the ground and you have your answer. I managed to destroy the first tube with the Sword-Claws, from there on out it was luck & remaining shield, which kept me alive. Oh yeah, the iconic butterfly boss (Evil Core) is hell, too.
Stage 9 (Wall) is my favorite stage, top level design here. Loose your remaining shield in the beginning to get another one just at the start of this stage and just have fun with all the traps, narrow paths and laser-pointers. The final boss (Armament Claw) is the second toughest in the game, expect to leave a fair amount of extends here.
The following epilogue (Versus) is quite relaxing, because of the many items you get here, including extends. Just remember that the four clutches (two on each side) of the bosses (Faust) final form, which let him climb up the shaft you'll fight him in, won't hurt you. Use the space to dodge at will.