CygWin - this uses cmd, but is probably the best environment that is GNU Linux like for Windows. You can use other terminal emulators to call on this; Mintty for example.
Windows 10 has Linux Subsystem - However, I haven't used this, but some swear by it.
Personally, I'd install VirtualBox and then download a GNU Debian ISO and install Linux into a Virtual Machine. Then, you can SSH into it and have a full blown Linux at your disposal, root and all. Putty and other terminal clients can then be used.
Mintty is a pretty decent terminal emulator that just works a hell of a lot better than the default cmd/conhost.exe, and it's basically mandatory if you want Cygwin to work. Wsltty is that but for WSL.
The default is just bad once you've used anything else. Copy/paste is the biggest flaw and this article says they're addressing it, but there's still more. The resizing still feels off, opening URLs is a hassle, the scrollback feels awkward to use due to some odd scrolling rules, the hotkeys are rather unique and largely feel counterintuitive to anyone who's used to any X11 terminal emulator, and more complex ncurses apps have a tendency to look wrong.
ConEmu is the same thing except with much more functionality that hasn't been particularly stable in my experience. People tend to like it because it does tabs and tiling and all kinds of fancy stuff.
Are you a laptop or desktop user? Do you really find the top-end 15" retina MacBook Pros to be under-powered? As for cost, my employer doesn't happen to mind, and for a machine with a dedicated video card, high res screen, 16GB RAM, and 512GB SSD the machine really isn't a whole lot more than any other similar-priced laptop. A few hundred dollars means nothing to most companies.
Have you considered running Linux (serious question)? I'm running Fedora at my job and it's been working great. I also have a retina 15" MBP and it runs great, I just got tired of not being able to use GNOME 3. Linux on Apple hardware has gotten a lot better.
Personally, I think Putty is a pile of shit. It's fine for 1-off things but beyond that it's horrible. I've had some luck with https://mintty.github.io/ on Windows but I'm not sure what it's full feature set it, I tend to not use Windows for much besides .NET development and gaming.
those look like formatting codes. if your console program supported coloured text of that type, those wouldnt be visible
for example, if running the app in https://mintty.github.io/ MinTTY, they would instead change the color of that line to indicate error/warning/info status
Don't confuse true colors which is the 24-bit RGB colors and 256 colors which represents 0.001526% of the true color space.
Real true colors in terminals are currently supported by mintty with these kind of ANSI escape codes:
printf "\x1b[${bg};2;${red};${green};${blue}m\n"
That said, I am not sure if vim supports true-colors terminals.