Below You will find list of bases/platforms where You can find tasks. Just add their location as a new GPS point (if You don't know how to do that, check the FAQ section at the end of this post). When You will get there, use a shining button near orange GPS point to start a task.
If there is no annotation that base or ship is pressurized, You should use a ship which is pressurized or at least recharge Your O2 before travelling there.
Order of locations is mostly random. You may want to add all GPS points, plan optimal route to a few of them and hide the rest. You may also check this almost handy map: https://www.geogebra.org/3d/zyeyynkg

Location: X: 117, Y: -122, Z: 9
Tasks:

• Survival Kit
  
• Hydrogen and Oxygen
  
• Mining
  
• Solar Panels

Ships:

• Starter Ship
  Notes: Pressurized, Ion Thrusters

Ores: Iron, Ice, Silver, Gold
Notes: Survival Kit with Energy; O2/H2 available after finishing tasks

Location: X: 421, Y: -394, Z: 173
Tasks:

• Ship Mining

Ships:

• Mining Ship
  Notes: Drills, Ion Thrusters

Ores: Iron

Location: X: -44, Y: -17, Z: -323
Tasks:

• Ship Tools

Ships:

• Blue Constructor
  Notes: Welder, Grinder, Ion Thrusters

Ores: None
Notes: Uranium Ingots; Assembler, O2/H2 Generator and Hydrogen Engine for deconstruction; partially complete Survival Kit

Location: X: -2006, Y: 3655, Z: -2685
Tasks:

• Pressurization

Ships: None
Ores: None
Notes: Pressurized after finishing task

Location: X: -1070, Y: 142, Z: -5041
Tasks:

• Ship Tools

Ships:

• Blue Constructor
  Notes: Welder, Grinder, Ion Thrusters

Ores: None
Notes: Hydrogen Engine for deconstruction

Location: X: 1634, Y: -5143, Z: 361
Tasks:

• Ship Building

Ships:

• New Ship
  Notes: Gatling Gun, Ion Thrusters; available after finishing task

Ores: None
Notes: Survival Kit with Energy; Hydrogen Engine, Hydrogen Tank and Large Storage Container for deconstruction

Location: X: -4523, Y: -3514, Z: -7747 (a ship near asteroid)
Tasks:

• Hydrogen Thrusters

Ships:

• Damaged Hydrogen Miner
  Notes: Drills, Pressurized, Hydrogen Thrusters, Small Reactors

Ores: Ice

Location: X: -4686, Y: 2489, Z: -12959
Tasks:

• Remote Control

Ships:

• Damaged Drone
  Notes: Unmanned (remote control only), Gatling Gun, Ion Thrusters

Ores: None
Notes: Antenna for deconstruction

Location: X: -726, Y: -13699, Z: -2168
Tasks:

• Jump Drives

Ships:

• Exploration Ship
  Notes: Pressurized, Warp Drive, Ion Thrusters

Ores: None
Notes: Warp Drive is almost required in final objective (You need to travel 5000km).
After a task You will get location of a Hidden Base

Hidden Base
Location: X: -9367, Y: -11481, Z: -13965
Tasks: None
Ships: None
Ores: None
Notes: Partially pressurized, no Survival Kit to recharge Energy. This GPS point is location of entrance door.

Location: X: 2844, Y: -12928, Z: 5650
Tasks:

• Projectors

Ships:

• Small Grid (Fighter)
  Notes: Gatling Gun, Ion Thrusters

Ores: None

Location: X: -2274, Y: -7135, Z: 11152
Tasks:

• Combat

Ships: None
Ores: None

1. How to add custom GPS point?
   Copy text in Location grey boxes to clipboard. You can add new GPS point by opening Your inventory and clicking on the last tab - GPS. There You can click on New from clipboard. You should hear a sound of new GPS point as coordinates and name will be imported from clipboard text. Short note: too many active GPS points make a complete mess on screen.
   
   
2. What will happen when I'll complete all tasks?
   When all tasks will be completed, You will unlock GPS coordinates of pirate base on nearby planet. Your objective will be to attack it. What it really means, is that You will have to cut off it's power in any way You choose. It has 3 Wind Turbines and 1 Battery.
   After You "destroy" pirate base, You will unlock GPS coordinates of pirate boss ship. Your objective is to attack it (cut off it's power; it has 1 Large Reactor). When power is off, You will see message popup and scenario will be finished.
   
   
3. What about Planetesphobia achievement?
   If You want to get Planetesphobia, You cannot enter planet's atmosphere. It means that You probably have to attack the base with remote controlled drone (if there is another way, please share in comments!). I've made second ship (remote controlled, prepared for atmosphere and gravity) and connected it with Mayday Ship using Connector. It will not detach when You use Jump Drive.
   
   
4. What about It Takes But One achievement?
   To get It Takes But One, You have to finish whole scenario without death. Most risky parts of scenario are Combat task and final objectives. If You'll use remote drone on planet surface, this part is not much of a problem.
   
   
5. Where can I find some resources?
   Aside from ores listed above, You can find lots of Uranium, Iron, Nickel, Silicon, Cobalt, Magnesium, Silver and Ice on asteroids near following GPS point:
   
   GPS:Resources:-2956:-15470:-8586:
   Thanks to Thertex for tip on that!
   
   Also, if You're on Your way to the planet already, You may want to stop by at Hidden Pirate Base:
   
   GPS:Hidden Pirate Base:1030612:-1939913:-2489183:
   Base is protected by 4 Gatling Guns, 1 Missile Launcher and 1 Interior Turret (inside Bridge). Base is pretty much useless, but on asteroids around, You can find almost every available ore (except Uranium though).
   Thanks to HumbleCanoe2 for the tip!
   
   If You're already near the Pirate Planet Base, You can salvage two damaged ships:
   
   GPS:Damaged Ships:1525282:-2843497:-3765303:
   If You need some Uranium, You can mine some at:
   
   GPS:Uranium Asteroid:1521808:-2839875:-3762952:
   Thanks to thameron for info!