A not particularly original quadcopter project

bms001:
I will probably try with cheaper components at least to begin with just to see where I can get to since my current goal is more around my own learning. I realise that this does seriously limit what the end product is capable of and I don't want to be doing the cheap basic versions forever.

That's understandable.

One thing I will say (based on my own experience) is that you end up paying more when you try the cheap stuff and learn the components aren't what you need. I've had times where I spend money on an IMU like an MPU6050, when later on I realize that I needed a BNO055 in the first place for what I wanted to do. Same with my altimeter, flight controller, servos.......etc. Look for what's best for your application (after doing extensive research) and then make a responsible plan on how/when to pay for it. I promise that in the long run, you will be saving money and getting better performance.

bms001:
Yeah I will probably go for the Teensy in the near future. I have an RPi kicking around (never used before) and wanted a project for it but I have some other things in mind for it now. Later on I may add it to a Teensy based QC as you suggest.

I use the Teensy 3.5 for several undergraduate research projects as well as for my RC plane. I can honestly say that that MCU is the best one out there in terms of hobby grade stuff. It has amazing processing power, has a fast clock, several serial/I2C/SPI ports, 16bit ADC, 5V tolerant, and is affordable. It's also really easy to use since you can code it using the Arduino IDE.