On auto/mines:
Realize that automines cost twice as much as their manned counterpart. This means, that for the same cost, mines will be as productive on a mineral with 0.5 accessibility as automines will be on a mineral with 1. No, this does *not* mean I recommend to never build automines, but automines should not be your default type of mine to produce. Even during the start of a game, when you're facing the impending mineral crashes that will occur, the decision to produce automines still relies on whether Mars has reasonable quantities of minerals with decent accessibility. Only after you know that it doesn't, should you start producing the automines that will help minimize the lost production time that may occur once Earth burns through its resources.
Ship based mining:
As Metalax mentioned, mining modules are actually the cheapest way to mine asteroids and comets. The problem mining modules have, of course, is that exact restriction. However, asteroids can be surprisingly lucrative if you take the time to survey'em. Just looked at my current game, and a quick check of asteroids shows one with a solid 288k duranium at 1. The other minerals are incredibly poor (Only 15k uridium at 0.9), but duranium is generally what an empire is shortest in, so it's still a pretty damn nice find. Also, this is before a team has had the chance to survey the asteroid.
As far as what one should use to transport the minerals, it depends on a few things, but if you're dealing with the inner asteroid belt in Sol, I recommend to simply send a cargo ship to pick up the minerals when there's a full load waiting. However, if you're experiencing a chronic shortage, mass drivers do provide more immediate access to minerals produced. This recommendation stems from the fact that mass drivers aren't exactly a quick build early on.
Also, you can use tugs to move the miners if you want to cut costs even more by getting rid of the engines entirely.
Oh, and one of their biggest advantages when compared to automines: They aren't produced by industry.
Last comment re: mining ships: You also double up on bonuses. The naval officer's mining bonus increases the effective number of mining modules and the civilian administrator's bonus applies to that modified value. Unfortunately, the same doesn't appear to hold true for terraforming modules.
A minor correction on cargo size that hasn't been corrected yet: Research centers (And GFTFs) take 100 holds to transport, not 25 as was previously mentioned.