If you're just starting: Border Skirmish, the only downside is you lose Turf (but 1 Turf is practically meaningless). Basically, you're looking to do as much damage as possible on your first turn. Ideally you have more fighters and you have the initiative: this should result in 1 enemy casualty (at least) with the enemy bottling on a 5+ or, if you went particularly well, even lower numbers. Don't be afraid to bottle early: you're basically hoping that you get lucky with Crew Size and Priority and even then you've only got a very brief window to win it (on average a 10 fighter gang will have all their fighters on the board after 3 turns).
If you've been going a while ask yourself what will benefit you the most:
A) more creds? Border Skirmish, Sabotage or Looters*
B) taking out some of your opponents fighters? Ambush
C) taking out one of their Special Territories? Sabotage
The other question is, what sort of gang are you?
For the Underdog to win at Border Skirmish you need to push HARD early. You want to make your opponent Bottle before they have a chance to bring their numbers to bear. Even if they hang around to fight it out, there's a fairly good chance that you'll thin there numbers through failed Cool checks (this mission doesn't usually involve friendly fighters being too close to each other, and may not see Leaders / Champs at all early). This means it's a good mission if your gang has some tools that can get you early kills.
For Sabotage to be effective, you really need a couple of gangers with 'bunker busting' weapons. +S CC weapons, Krak Grenades, Plasma Weapons etc are all ideal for this. Without those though, you're relying on weight of dice.... and you're likely to Raise the Alarm that way. Ideally, with Sabotage you blow the objective on the turn you Raise the Alarm and then just run. Don't try to fight the Sentries unless you have overwhelming numbers. If you don't have bunker busting weapons, perhaps Looters is a better option.
With Ambush: you need to be careful about who you Ambush. It's one reason why I advocate getting to 10-12 fighters early: you really want to have more than 8 fighters ready to go for an effective Ambush, or there's a decent chance you won't outnumber your enemy. Skills like Inspirational are HUGE in this mission: the ability to re-roll Cool checks means you're more likely to get 2 Actions. Equally, Templates / Blast is really your friend for this mission: the ability to take out / pin multiple enemy with a single activation allows you to continue pouring on the heat.
* I'm assuming you've house ruled the ability of the Defenders to Bottle in Looters and deny the Loot to the attacker.
What is your objective in this Turf War?
If you're middle of the pack, then you're probably not making a play for Top Dog. What you're probably trying to do is just crawl a little further up the ladder. You do this in two ways: first, you fight battles gain Rep, Experience and Creds; second, Gangs higher than you get crippled and fall.
I'd try to organise a fight with the people around my power level.
In a Stand-Off, if I'm fighting down, I'd try to:
A) keep my Champs/Leader alive (the surest way to drop is to lose a Leader / Champ)
B) maximise Rep gain
In a Stand-Off, if I'm fighting up, I'd try to:
A) keep my Champs / Leader alive (yup, no change here)
B) take out my opponent's Champs / Leaders (even if you don't get lucky and kill them/Critically injure them, simply stopping them working is a significant cost)