Welcome to the forums!
I am also using Sterilite for some of my pieces right now, except I'm using a heat gun. I have some pieces that retain the shape I want them to, and others that just keep flattening out. I've found that the ones that are flattening out are the bigger ones, which I've rested lying down. I've gotten better success "standing" them up or tying them into shape with something and leaving them overnight. You have to be sure you're holding them overshaped for several minutes until they're cool enough to touch without gloves (I don't use cold water, though). They also seem to generally hold their shape once I've got primer and spray paint on them.
Even still, they'll soften back to their original shape eventually. Honestly, Sterilite is a tough material to work with because it's made to retain the original shape it had. Great for beginning kits to learn, but not the most preferred.
Another cheap way you might consider is looking up local sign shops (like FastSigns) and asking them for Sintra scraps. Sintra is so much easier to work with. I got a stack of scraps big enough to make a set of basic plates from my local sign shop for $5, although you can usually get them to give it to you for free.
