I have posted this in the Tips & Guides section but please see below:
Edits and additions more than welcome from the community.
In Marine Arena, its all about getting more kills from your opponents than your opponents get from you. Holding the high grounds and always knowing what your opponents are up to is a must, this way you gain an edge over your enemies, giving you chances to ambush or snipe their units.
Your Infested Saviors are your "last chance" of defense. You only get 2 to start, although you can purchase more from Arena shop, its expensive, so use them wisely. If you can get away with using turrets or base defenses against a small army, then dont waste a Savior. (On Sudden Death Mode you want to use all 2 in less than an hour however.)
Mercenaries can be very useful when used right, but they also have counters, be sure to choose the appropriate Mercenary for the job, dont put Stalkers against Phantoms. Read the tooltips on the Mercenaries for examples of their Good and Bads.
Marines are your main units, dont neglect them unless you're sure you're not going to use them. Marines are your quickest, cheapest, (and early game) are your weakest units. Mercenaries may encourage you not to use them, but the "Teched Marine" always ends up on top in Marine Arena, it is just difficult and requires some micro-management skill to get them there.
The Teched Marine strategy starts with Armor and Range. Get your range up high enough to shoot over your and you got yourself a nice Mercenary Meat Sheild to cover those Marines. Increase your weapons damage as your opponents increase their armor, slowly bring all upgrades up to max and your Marinesare unstoppable and give your opponents very little bounty for their hard efforts to stop them.
Going straight to high Mercs can be an early game ender for your opponents, but can also be a problem for you if your opponent survives to get your counter, because you will have given him huge amounts of minerals for killing your high Mercs. If you plan to do this beware of their Savior count, and beware your units' counter doesnt pop up.
Armor is an essential upgrade. If you can tech your Mercenaries or Marines armor past your enemy units damage, they can become an unstoppable army. Note the Armor of your opponents however, if they're teching armor too, you should get yourself some damage upgrades.
When it all boils down to the basics, you have two choices... Marines or Mercs. Although the Heroes do have their uses, investing entirely only into heroes can sometimes be a bad idea, unless you've developed a solid plan for them. The Ghost is a "hero-killer", although he may have some other uses, using him solely for killing normal units isn't always a good idea.
If you've got a problem against Teched Marines, consider high damage Splash Mercenaries or Heroes. Banelings are always good ambush defenses, and teched Mutalisks should also do the trick, since the Mutalisk is best vs. massed ground. But also upgraded Heroes like Colossus & Spellcasters like High Templar or Infestor can do the trick!
If you've got a problem with a turtling enemy, who just wont quit with the base defenses, try switching to particular Merc or Hero to finish the job. Late game, with the expensive Mercs out, some players are too stubborn to revert back to early Mercs or use Heroes to end the game. Remember, there are Banelings, and Odin or Nova Ultimate Heroes have high damage Nukes.