Yeah, levels are a kinda nebulous when it comes to RP and the question is what is the metric where you change your outfit. For example if you are doing missions does the general level of the missions dictate where your character is at along their personal timeline? Running DFB and have him start in his scrap suit? Running higher level taskforces and he's got better gear from his exploits as a hero? Thats going to be annoying, but interesting, to make all the costume slots for. Beyond that I wouldn't fret the level system too much, and would largely ignore incarnate status unless its specifically important to your character's backstory.
I tried to do something similar with Hawtdog, as her armor is entirely scavenged to the point where her boots dont even match. The idea I had was as she progressed she'd "acquire" gear with the various villain groups that she fought creating a mishmash armor set that tells a story of the groups she's run across.
The idea is good but I've found it hits a bump in implementation as unfortunately some of the armor pieces are either npc only or, for the purposes of Arachnos, tied to the Spider Archetypes.
As for "outside support" in the form of equipment donations. Corporations/businesses are going to want to support heroes who are moderately well known, or better, and are known for being good for PR. The more you make a name for yourself, and the more that name is associated with good things, then corporations might lend/give you equipment. Just remember, you start getting bad press by doing, or being accused of doing, dubious things and that support might evaporate.
Another avenue to approach is the Super-Cottage Industry of Crafters. Basically think people who build custom orders for cosplayers except they make the real deal. Expensive? Probably. A state of the art neutrino edge on an axe always is. That doesn't mean you cant barter or earn it through favors. As your character does heroics he can do an Axe of Theseus where he gets a base axe, then gets someone to reinforce the handle, then reforges the head after it gets mangled, then adds an energy sheath on the edge because raw metal can only do so much. His equipment can evolve with him and while he doesn't just get a new axe, the axe he has at the end of the line is nothing like the one he started with.