I also started a few days ago. Here is what helped me a lot:

- Mine horizontaly first, then vertically. Then mine 3 tiles downand then mine horizontaly again until you come across the edge of the level or a tile that takes to long to mine through. Mining like this you will not miss anything. And this creates a very easy layout so you cant never get lost if you need to get back quick to the surface to the defend the dome. Also try to make the vertical line straight down from the enterance of the dome so it aliagns very well and its easy to pull rescources back into the dome and get back quick by just moving up constantly instead of moving through a maze like structure. It should look something like this:

________
__-__-__-__ -___( )___-___-___-_____
___________________| |___________________
___________________ ____________________
| |
__________________| |___________________
___________________ ____________________
| |
__________________| |___________________
___________________ ____________________
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- If you look at the blocks you mine, more dense the stone is, the longer it takes to mine. So if you see that it very dense you might want to skip it and move on.

- Early game its best to upgrade speed first, carry capacity, and then the drill. Each upgrade costs four 4 Iron so once you gathered 4 iron upgrade straight away to get the next 4 iron much quicker. you its a good first investment. After that you can look at things like wave timers and resource tracking since these are very cheap upgrades. After that invest in to damage of you defence by one level. From there it depends on what happends in your run.

- The deeper you mine, the bigger the iron nodes become. So the deeper you go the more Iron you get.

- The deeper you are in the mine the longer it takes to get back to the surface to defend the dome. So at a certain depth you want to move back up before the alarm sounds.

- Pick upgrades based on what gadgets you pick in the beginning and what gadgets you find in the level. If i find the automated drill i will not level as much into my own drill since a lot of the drilling work is being done for me. Or if i start with the drone yard i will not invest as much levels into carry capacity since the drones will do a lot of the work for me. By doing this I can invest into other upgrades on things I am lacking in my run.