I didn't bother upgrading my mines above level 12 (uranium I had at level 14 at that time) before starting to build my explorer/shipyard skills to start looking for more planets. Once you find one the buildings actually level up really quickly since you already have the skills leveled up. Having a 2nd planet pretty much doubles the production, once you have 3 or 4 it's also worth to start upgrading the research skills.

good thig you have your depot already at level 12 as you will need that to upgrade the mission control which allows you to send out more ships at once.

Good luck with the grind.