I assign each mineral a point value based on near-and-long-term strategic importance.
Surveyed bodies have a point total, which is the sum of each mineral's accessibility times its point value (only counting mineral deposits above some minimum quantity--typically 2k).
I then prioritize mining operations based on:
   Mineral point totals.

   Total cost of ownership.
      Orbital mining modules are the same cost as surface mines, but are quite a bit cheaper to transport and do not require population to operate.
      I will therefore tend to prefer to use orbital mining first.
         I prefer to cap my initial mining rate per body at 10% of the size of the most significant deposit (CRN or DUR, usually).
         That way I can leave any given orbital fleet in place for 10 years before needing to relocate.
      When I have established operations at all desirable orbital targets, I will establish surface mining colonies on low-CC worlds with valuable deposits in systems that I can safely add to the gated network.
         I usually will seed such a colony with enough infrastructure for 500k population.
         Then I rely on the civilian shipping companies to deliver population and more infrastructure.
         If the body has a low population cap, I will try to deliver surface mines to keep up with growth.
         If the body has a high cap, I will deliver a few mines at first, and then construction factories so that the colony can bootstrap its own growth.
      Automines are terribly expensive. I will use them only as a last resort.

   Proximity to production centers.
      Early on, proximity to homeworld is the primary factor.
      The creation of new production centers increases the viability of nearby mining locations.

   Overall system richness.
      Logistically, it is more efficient to develop multiple sources in one system than to spread development out over multiple systems.
      It is also beneficial to deploy orbital mining operations in systems with numerous orbital targets, to minimize the production time lost when redeploying as bodies become depleted.

   Diversification.
      Logisitical efficiency notwithstanding, it is a good idea to avoid putting all your eggs in one basket.
      If you've ever seen your empire's entire economy come to a screeching halt after losing your only fleet of Sorium harvesters to a pesky spoiler fleet...well, you probably don't want to see that happen a second time.

Usually, in Sol for the early game I will look to secure at least one high-quality source of duranium, corundium, and gallicite, perhaps two each if mineral rolls are nice to me. Sometimes you can get multiple of these from one body, oftentimes you will need a different comet or asteroid for each one. Other minerals tend to be found in sufficient quantities incidentally until later in the game.

Otherwise, in Sol I leave other bodies available for the CMCs as these are an economically efficient way to diversify your mining assets. You only need 1-2 sites for each key mineral in Sol so that you can force those mines to grow in output as needed once Earth starts to be hollowed out, since CMC growth is not predictable nor controllable.

Once I am expanding to other systems, I will place mines as needed based on my economic goals. A fleet base may have a few dozen mines and/or some asteroid mining operations to provide minerals for MSP and fuel production, while a major forge world several jumps from Sol may have hundreds or thousands of mines distributed across that system and its neighbors to maintain resource independence. At some point, you will run out of minerals in Sol, and all the mines you have (plus the many more you should be building) will have to go somewhere - if you find a planet with very good deposits in a key strategic location, it makes a lot of sense to put 600 mines there.

Don't worry too much about if the scale you are playing on is "right" - just play and adapt as you discover more of the game. For the record, against the NPR you will probably find that ships <10,000 tons are suitable for escorts, ships >10,000 tons as capable cruisers, and ships >20,000 tons as capital ships which lead your fleets into battle - but this is not set in stone at all, it is simply one reasonable possibility. I often like to build my ships much bigger than this, but in a conventional start you might find smaller ships to be more practical. Of course tonnages can evolve over time as well and there is no need to commit to, say, 17,875 tons being "cruiser size" for all eternity.