Ok, let's start from this that I don't realy like idea, that you can buy in store things like boots, armor, weapon etc. It's sometimes just not logic. I know that there was in Dota like this, but I heard already so many things taht this game is other, that I think it is chance to make something better.
If I buy helm for my character why he is not wearing it? This same with armour and other stuff... If I am buying something I would like to see it on my character. Other thing is that it will be ridiculous sometimes, let's buy leather boots for... Rook. That's stupid in my opinion.
1. First idea 
So I think it could be better if instead of this standard stuff you can found in stores there would be something like magic crystals, which you are using to "plug" to your actual stuff.
Let's say you start with standard equipment. Exactly how it looks right now. But in stores you just buy crystals which are inserted into your armor, weapon etc.
It of course doesn't change anything right now in game, but for me it is much more logical. Also it explains why Demigods don't change their look.
2. Second idea
I think that there should be limit of specifying items you can use. I used to play Dota, and it is a little stupid that you can buy let's say 6 pair of boots. I think it would be better if there was a limit. You have a view of your character. Then you can buy just one pair of boots, one armor, two weapons (or weapon/shield) etc.
If "First Idea" would be used then we already have our wear, and we just have slots for our magic crystals. But still we can't buy 6 crystals for boots. But just one for everything.
3. And last Third idea (only if "First Idea" would be used)
There could be diffrent number of slots for each character. For example The Rook could have more 2/3 slots at his torso, but without slot on boots or head.