True, you can, but if your directions at the title screen were too subtle, you have to listen to Alia bitching at you when you start a "wrong" level.
God, I hate that aspect of X5...
MM1: I can't argue with the "intent" of CutMan given that he flinches to the Mega Buster, but Guts Man is the far wiser choice. Every attack can be seen a mile away and his ability is needed to nab the Magnet Beam.
MM2: Air Man. Slow attacks and double damage from the Mega Buster lets you trade hits with him very easily, and he gives you Item 2.
MM3: Top Man is obviously intended (double damage from Mega Buster and ludicrously simple attack pattern), but I prefer to start with Needle Man. His stage has an easy E-Tank to fall back on if needed, and Rush Jet is too awesome to start anywhere else.
MM8: Grenade Man. Rush Bike is a small but useful crutch.
MM9: Splash Woman. She's marginally easier than the others, and has a nice straightforward weapon.
MM10: Um...totally not Sheep Man?
X1: Yeah, can't argue with Chill Penguin. Might be worth mentioning though that the entire rest of the armor comes at the end of the game if you follow the weakness order from there, so immediately after Chill I break and go to Sting Chameleon. Body capsule is plenty to see me past him.
X2: Tough choice, but I'd say Wheel Gator. His attacks are slow and his weapon is necessary to reach a number of secrets.
X3: Yeah yeah, Blizzard Buffalo, leg capsule...
X4 (X): Web Spider, ditto.
X4 (Zero): Magma Dragoon. Besides the whole Ride Armor thing, Ryuenjin is a crazy powerful and useful weapon, necessary for a few Heart Tanks as well.
X5: As far as the "intended" order goes: You know its Grizzly, I know it's Grizzly, the Bat Bones crapping on Capcom's roof know it's Grizzly.
X6: I know the popular vote is Commander Yammark, but I MOST DEFINITELY must stand against it and say Blizzard Wolfang. Easy boss whose weapon is invaluable when navigating the game's many tricky hazards, and is also key if you place higher priority on Shadow Armor than on Blade (and since we all know that Blade is crap anyway...). He also has probably the least annoying Nightmare Effect.
X7: Despite the extra health of his Ride Armor, I'd say Vanishing Gungaroo. His attacks are easy to evade and his weapon gives Axl some much-needed firepower.
X8: I've been New Game Plus-ing this one so long that I'm not really sure who's the best to tackle with limited health. I guess one of the vehicle levels?
Xtreme2 (X): Neon Tiger. As tempting as it is to tackle Catfish for the leg capsule first, he's an extremely annoying boss, and the Ray Claw will bring him to his knees (plus it's useful against Launch Octopus as well).
Xtreme2 (Zero): Objectively speaking, I'd say Tunnel Rhino. Simple boss, crazy powerful weapon with unlimited use, and necessary to get the body upgrade. But, I tend to go Blast Hornet just 'cuz I'm an Earth G. addict. Truth be told, starting with anyone other than Wire Sponge really should be a safe bet.
Zero1: Maha Ganeshariff. Weak to thunder, and you need to beat him before you get your extra weapons.
Zero2: ...I guess Hyleg for the loose Sub Tank.
Zero3: Childre Inarabitta. Throw Blade is just too awesome not to.
Zero4: I don't think there's a clear winner in this one. Maybe Pegasolta Eclair, since Ice Z-Knuckle weapons are easy to come by IIRC. But I'd just as easily start with Heat Genblem or Noble Mandragoro.
ZX: Hivolt for Model H, obviously.
Advent: Not much of a choice, but I'd say Chronoforce, since his charge attack is so insanely broken...