Every base you build will cost you twice the amount the one before it did. This is a never ending rule that just keeps on increasing to infinity. However if you delete one of your bases the next one will cost 25% the cost it would have. Bases Prices: 50 - 100 - 200 - 400 - 800 - 1600 - 3200 - 6400 - 12800 - 25600 - 51200 - 102400 - etc
This entirely depends on what you are looking for the astro to do; production of fleet (production), boosting your economy, research, etc. For economy, you should be aiming for either an Asteroid or a Crystalline, though the latter is generally rare and hard to find. If it is a production base you want, Rockies are the best, though Metallics and Craters fill this role well too. Usually you will want to use a Gaia, Earthly or Arid for research bases, due to their large area and high fertility, though they suit most tasks pretty well.
If you want to build another base, build at an outpost ship. After you have a good location for the base, move the outpost ship (it is usually good to escort the outpost ship with some ships) to where you want the base. Go into the fleet where the outpost ship is, and click «Build base».
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