I don't even have my costume finished yet, but I think it would take an extra pair of hands maybe.
My best guess: flightsuit-> boots-> spats-> neckseal-> vest(if your armor is already attached to it, it'd be easier)-> belts-> backplate-> knees-> gauntlets->cape-> jet pack-> gloves-> helmet. ???
Hahah I really don't know, hopefully somebody with a completed costume who's got the order down to a science will come along and let us know. I'm also wondering. But I think it is just trial and error, and what works best for you. Again though, having somebody help you out probably makes it a ton easier.
1. Jumpsuit
2. Boots
3. Tie Ankle Ties
4. Place Shin Tools
5. Attach Knee Armour
6. Attach Cod Piece and Kidney Plate
7. Attach Girth Belt
8. Attach Hip Pouches
9. Attach Ammo Pouches
10. Attach US Divers Belt
11. Attach Jet Pack Harness
12. Attach Vest with Armour
13. Attach Jet Pack
14. Put on Gloves
15. Put on Gauntlets
16. Put on Helmet
As for wearing anything under the suit (besides my boxer briefs) nothing unless it's an outdoor event in the middle of the winter. Then MAYBE I'll wear a T-shirt under it...otherwise never. It's too hot!