Auto-crafting is a godsend. It takes away the worry of having to click those bottles constantly, and guarantees a seamless transition from one craft to the next. I'd call it the most important thing to buy early-game, it allows you room to explore the UI and learn about other features that will become pivotal in your growth.
Any good person of business knows that the best business isn't the one that makes the most money, but the one that bother you least.

Auto also continues its diligence while you have the game closed, that's where you make the big profits, allowing you to claw your way to the next big upgrade and get your growth engine running again.

The importance of auto scales up as you begin to prestige. It will take care of the early game admin for you, researching flasks and buying slots instantly. These important upgrades are bought with fire.

Fire will get you the best upgrades. The main issue is how slow fuel gain is. A quick look at the system shows you that the way to acquire fuel is to prestige and research. All you need to do is constantly prestige as efficiently as possible.

Research all flasks that you can do in a very short time. Your wall is where you quickly find yourself having to wait much longer to research, e.g. it may take 40 seconds to research up to blue, but purple may take a good half hour. Ideally at this stage, you should hit your wall in under the 1 minute prestige cooldown timer.

Prestige and keep prestiging as efficiently as possible, gathering as much fuel as is proportional to how long you have to wait for it.

Eventually you'll be auto-prestiging and researching flasks. It's important to note that auto-prestige only works when you're in the current save. It will not work if you have the game closed or are in a different area, e.g. flask auto-prestige will not happen while you are in tubes.

The upgrade to burn faster is a 10% boost at the cost of 250 fuel, so you should wait till you have 2500 fuel before you begin to buy this.
You should never lose more than 10% fuel for a 10% gain.
If you have Freeze Mode unlocked, fuel earned there can only be used to upgrade burn speed, and is wasted if you do not, as the upgrade carries over but the fuel does not.

Above is the best fuel growth prestige strategy. The best economic growth prestige strategy is highlighted in Adventure Capitalist with the angel investor mechanic, very similar to the golden flasks gained from prestige in this game.

In Ad Cap, each angel investor gives you a 2% upgrade, here each flask gives a 10% upgrade.
In Ad Cap, it is best to reset once doubling your investors.
If we take that proportionally, you should reset once you have a 20% gain in flasks. However, this game obviously has different confounding factors affecting the best prestige ratio.
I'm unclear on the best action here, I don't know the maths.
I've been going with prestiging when I've doubled my flasks, it may or not be optimal, but it's been working pretty well for me. I'll update this if someone knows better.

It costs increasingly more to get upgrades. Your saviour here is the reset upgrades button, allowing you to shift your multipliers when necessary. Investing in fire gain early for strong upgrades is extremely strong, and you can get your diamond flasks back when you need them for a prestige multiplier, etc.

Generally, I store my diamond flasks in the extra energy upgrade, with a few in upgrades such as fire and prestige gain. It is a large straight-up multiplier and the cost doesn't scale.
Remember: money not spent is money wasted, always have your flasks spent in something.

Try to always play the daily solitaire for diamond income, also solitaire is pretty fun.

I'll add to this as I play more of the game and learn more about it - I'm a beginner myself.
Good luck to my fellow gamers out there.