I've tinkered with arduinos and stepper motors/stepper controllers. I built a CNC mill. But I'm hoping there are components that I can plug together and just focus on the software side using existing hardware modules.
I'm a web developer who got the bug to get into robotics about four years ago as a hobby. I ended up joining a FIRST [1] robotics team as a programming mentor and I've learned a lot [2].
ROS is a good platform for writing software. There are ~50 hardware platforms that support it. Unfortunately robotics is still built to a purpose, and usually a bit too expensive for a typical hobbyist platform. Our latest robot here at Duke was built with modularity in mind and still cost well over 100k.
It's not really necessary to use turtlebot, you can use ros with whatever you want, it just won't work off the shelf. Setting up your own robot with ROS is a great learning experience and a great way to get familiar with it.
ROS, ROS, ROS
all our robots are on ROS and you get visualization and simulation tools, 90% of the things you'll ever need come from apt-get (ubuntu make everything easier) but the real deal is Gazebo and stage for simulation and the wiki is full of tutorials
I wanted to get into robotics as a way to get up to speed on neural nets and reinforcement learning. I found the Lego EV3 kits to have a good mix of sensors motors and supporting parts. The EV3 bricks run Linux, there's a distribution for them called ev3dev, and they'll even run ipython notebooks.
I'm now looking at getting a BrickPy for it as the EV3 brick doesn't do FP, so not good for NN's.
I would skip your search for the "right stack" and think about working on real, profitable applications. Develop whatever needs to be developed to solve a real problem. Most things calling themselves 'robotics stacks' nowdays are overblown and add more complication than they're worth.
Take a look at vexrobotics.com. They have all the mechanical and electronic parts you'd need to build small-ish robots (think Roomba size or a bit bigger.
Edit: actually they have a VEX Pro line too that's aimed at larger robotics too (primarily designed for FIRST and BattleBots).
[1] FIRST http://www.firstinspires.org/robotics/frc
[2] https://www.youtube.com/watch?v=8319J1BEHwM