Once upon a time, a complex timing waveform generation like the horizontal and vertical TV sync pulses, were designed using only vacuum tubes. But the sync generator was a refrigerator-sized cabinet.
Then it went to all transistors. But the generator still used a 4U 19 inch rack plus a large external supply.
Now everything fits in a 2mm X 2mm VLSI running from a pair of AAA batteries.
The point I'm trying to make is: do you want to build a practical circuit, or do you want to do it the hard way, because of technical curiosity or as an academic exercise?
There is nothing wrong with the latter, I sometimes like to build such circuits simply to satisfy a technical challenge, to exercise my brain. But those circuits are not practical.
Now, if what you want is a brain challenge, start with the basic circuit that Brad has suggested. You will find however, that as frequency increases the transistors will require matching and a you'll also means to prevent them to saturate.
The output waveform will look like crap, so you will require to follow them with a schmitt trigger and a monostable to maintain the duty cycle. You will not able to load the ST output because that will change the operating point. A totem pole buffer will then be required.
Then as the devices warm up, you may find that the pots require constant tweaking.
I AM NOT ATTEMPTING TO DISSUADE YOU! QUITE THE CONTRARY, when one builds such circuits, one gains an enormous amount of insight on actual circuit operation. One gains significant admiration for the engineers of yore, which were able to design and build complex systems like computers, Radar, TVs and oscilloscopes with only discrete devices. It is a real eye opening experience.
OTOH, if you require a practical device, use an IC or two.