So your basic question seems to be: Surge or Promote? This is a rather strange question as those two summoner spells fit very differently into the current Meta-game. In fact, I don't believe there is ever a hero I could imagine having to choose between those particular spells as they serve very different roles. So instead, let's assume that you want to know when these two spells are appropriate (and not make a choice between them).

Surge

Surge is a rather recent introduction into LoL and is still having its place in the meta-game examined. While it does act as a much needed steroid for a number of champions missing one (eg. Twisted Fate or Teemo), it suffers on champions who require a lot of farm (i.e. most carries). In comparison to spells like Ignite and Exhaust, Surge (while scaling better) just doesn't guarantee kills the same way through early/mid-game. Now, it's true that Dominion has a shortened early/mid-game, but it's just as true that it has a shortened late game (where this spell really shines). As a result Surge is frequently not the best choice for champions (even carries).

• When to get it? When you're the main DPS and you don't have a built-in steroid

• When to avoid? When you're a carry who needs kills to make it to late game

Promote

Promote is another spell which hasn't yet found a good place in the overall meta. However, having been around longer, there are more obvious cases where people use it (i.e. in Dominion going bottom against a Champ who has trouble clearing lanes early on, like Tryndamere or Yorick). Given Promote's role in taking down towers, it's no real surprise you see it more often in Dominion than Summoner's Rift. Usually, you want Promote to push your creep wave into a tower allowing for a better engagement at a node. This frequently means you find Promote on Champions who have trouble clearing lanes or who are good initiators. A Champion that requires more farm or is main DPS (i.e. a carry) is a less likely place to find promote as it doesn't fit their role well.

• When to get it? When your team lacks a lot of lane clearing ability (or against a team which lacks it)

• When to avoid? When you're filling a more important role (i.e. Carry)

Garrison

I'm surprised you're reading a lot of information that Garrison is a poor choice; it is quite a good spell. The problem with Garrison is that it really only shines is defending nodes in Dominion. Very frequently people don't do this (usually because it's less exciting). However, there are a large number of places where your team can really benefit from Garrison (solo bot, or even defending top). Garrison can break a channel (from further range), stop a wave push, or even heal a node, all very useful things in Dominion. Even if it only forces the other team to break off an engagement then it is directly translating into victory points (something few other spells do).

• When to get it? When you're running a 3 Node defensive strategy or against a team with a lot of floaters (e.g. Rammus)

• When to avoid? When you're filling a more important role (i.e. Carry) or you're going for a more aggressive strategy (i.e. running floaters)

Flash vs Ghost

Both of these are excellent spells (and there are even times when you might get both), but in Summoner's Rift, at least, the current meta-game has stabilized on Flash being invaluable. This is largely due to two factors:

1. Flash lets you get out of (or into) range of abilities and champions
2. Flash lets you "jump" over the twisting terrain in SR

However, in Dominion both of these reasons are less effective. The terrain in the Crystal Scar has fewer features you can "jump" with Flash, the faster game play means champion deaths are less impactful (thus saving, less important). While still a great spell, Flash is nowhere as dominant in the Crystal Scar as it is in Summoner's Rift. Instead, two other features dominate The Crystal Scar which make Ghost a frequently more picked spell:

1. Non-linear attack routes
2. Contested towers

Having multiple paths to engage (and less vision) often means you are forced to move to positions very quickly. This is the reason champions like Rammus are so frequently banned. What's more, it's frequently a strategy to rush to the top tower at the opening of the game to assert the defender's advantage. In a rush strategy (fairly common) it is necessary that most of the top defenders have Ghost to out pace the other team. As a result Ghost may not enjoy the same dominance that Flash has in SR, but is still a powerful spell (and a frequent choice).

• When to get it? Both Flash and Ghost can be great spells on any Champion

• When to avoid? Only when you have something which is much higher priority or more synergistic with your strategy (like Zombie Karthas was).

You never stop to try and last hit the minions, except when you're playing support; then you'll leave the last hitting to the carry you are with. But at times it's good to push minion waves to the enemy tower (either using your spells or starting to auto attack), since enemy towers can and will deny gold (and XP - only when your opponent isn't there) from your opponent. But you always have to look at the map when you are going to push, because overextending and dying to a gank is worse then letting your lane opponent farm.

Conversely, if the enemy is pushing his minions closer to your tower, you can start auto attacking the minions to get them down faster, but even while auto attacking you still need to watch minion hp so you can get the last hit.