First off, this is a completely new brand, so we don't have any assets or design guidelines. Go nuts! Feel free to push me to consider things I haven't thought of.
I really like flat, modern designs that are easy to implement in code but look beautiful. This design will form the basis of a responsive app across many platforms, so please design it with a brand language that will execute well on the web / mobile, not like a poster.
In terms of specific ideas, one Idea I had was to play with the abstract concept of a coin, similar to the first attached reference (but with the full name in the middle).
Another idea I had was to play with the concept of a piggy bank with coins going into it, similar to the second reference.
Any other ideas you have are absolutely welcome. I am a programmer, not a designer, and am completely open and looking forward to being surprised with your ideas!
My competitors largely use green (trees, growth, money) or blue (professional, trusted, etc). I want to stand out from them, but I have no idea what colours would work well for an app that looks premium and modern but not expensive, and conveys that concept of trust. I'm quite flexible with colours, but do not want to sway towards a particular gender or demographic other than adults who want to get their lives in shape.
Also, I'm planning to use Sketch for designs for the app, so if you happen to use Sketch to design the assets I'd (optionally) love to get sketch files as well.