Sorry it has taken so long to post a followup. Here is an intro and the mining info for Liberty Space.
General Notes About Mining
Obviously it's easiest to mine in a system where you are at least neutral with the most common factions in the area. That way you can simply fly into the area to be mined, stop, and blast away without having to fend off bands of local nasties. I use the turret view when mining because you can easily swing around 360 degrees in almost any axis. I have found that regardless of which system you're in, there will be a battle going on somewhere nearby. Try not to accidentally shoot anyone and muck up your rep. Neutral ships can sometimes look like debris. When you're mining, don't bother shooting at anything which doesn't cause the cursor to turn into a "spinning wheel". Different graphics are used for the minable objects depending on what the field contains. For example water ice may look like spinning ice crystals or rock, and scrap metal looks like a spinning metal chest before you shoot it. Either way, shoot the object and tractor in what is left afterward - if anything. In some fields you may have to shoot many times before you get something you can tractor in.
You can try shooting at things while moving, but I find it easier to do mining while stationary - others with better hand eye coordination may prefer otherwise.
Mining near the bases of "criminal" factions can be hazardous - even if they are neutral they may decide that want what you've mined and demand you give it up. This is especially true if you mine diamonds in Dresden; the Red Hessians want all of them and will want them back!
Mining only gets really profitable in money terms when you get to the outlying systems such as the Tau systems - but the run back with the goods is long if you want to maximise the return. Also in many places, hazards like radiation make mining a waste of time due to the cost of repairing your ship. You're better off in those cases just buying the commodity at the cheapest price from a base and trading as per usual.
I've listed each system with areas which can be mined, and what you will find. I've also included any potential hazards - such as radiation or factions that may attack you. I've made a rough guess at what you can collect in 5 minutes but I haven't timed them so YMMV.
Mining in Liberty Space
Best Bang For Your Buck:
1) Pick up scrap metal in the debris fields in the Texas System and sell it at LPI Sugarland. You'll need to be at least neutral with the Liberty Police. The debris fields are close to Sugarland, so you can do many runs quickly.
2) Pick up silver in the Silverton Asteroid Field in the Colorado System and take it to California Minor. Although it takes a long time to collect silver, the return per unit is high.
California System
Sierra Ice Field (C3-E3)
Hit Rate: Good - 10 units of water in under 5 minutes
Hazards: Liberty Rogues, Bounty Hunters
Whitney Ice Field (F6-G4)
Hit Rate: Poor - 6 units of water in about 5 minutes
Hazards: Liberty Rogues, Bounty Hunters
Tahoe Ice Cloud (B5-D6)
Hit Rate: Poor - 5 units of water in about 5 minutes
Hazards: Liberty Rogues, Liberty Navy
Colorado System
Silverton Asteroid Field (D6)
Hit rate: Poor - 7 units in about 5 minutes.
Hazards: Xenos
Copperton Asteroid Field (B3-B5)
Hit rate: Very Poor - 3 units of copper in about 5 minutes.
Hazards: Xenos and Bounty Hunters.
New York System
Pittsburgh Debris Field (F3)
Hit rate: Good - 16 units of scrap metal in under 5 minutes
Hazards: Liberty Rogues, Junkers, Bounty Hunters
Detroit Debris Field (C4)
Hit rate: Very good - 20 units of scrap metal in under 5 minutes
Hazards: Liberty Rogues, Junkers
Texas System
Hazard: There is a radiation field close to the sun. It is marked with hazard buoys.
North Dallas Debris Field (D2-D4)
Hit Rate: Good - 16 units of scrap metal in 5 min (timed)
Hazards: Junkers, Liberty Rogues, Bounty Hunters
South Dallas Debris Field (D5-D7)
Hit Rate: Very Good - 20 units of scrap metal in under 5 min
Hazards: Liberty Rogues, Bounty Hunters
East Dallas Debris Field (E5)
Hit Rate: Good - 10 units of scrap metal in under 5 min
Hazards: Liberty Rogues, Bounty Hunters
West Dallas Debris Field (C4)
Hit Rate: Very Good - 20 units of scrap metal in about 5 min
Hazards: Xenos, Junkers
Best Prices
Copper
Liberty, Colorado, Pueblo Station $400
Scrap Metal
Rheinland, New Berlin, Dortmund $100
Liberty, Texas, LPI Sugarland $70
Silver
Kusari, New Tokyo, Planet New Tokyo $840
Liberty, California, Planet California Minor $714
Water
Edge Worlds, Omega 41 & Omicron Theta, Freeport 5 & Freeport 9 & Leon Base $240
Liberty Texas LPI Sugarland $70
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