Personally I don't like using Marines or Firebats. I feel that by the time you spend the resources to upgrade them enough to do any damage at all, you could have built a larger mechanized assault.

Go with at least 3 Tanks upgraded to siege mode. Tanks are useless unless you can get them into the right position and set them into siege mode. They do massive damage this way and when you put 3 (or even better about 5 of them) in a row, nothing on the ground gets close to them. You should always bring a few Goliaths along with your tanks for two reasons. If the enemy sends in air units the tanks can't shoot them but the Goliaths will. Also, if a ground unit gets too close to one of your Tanks in siege mode it cannot fire at it. The Goliaths machine guns should rip them up.

Air Offense:

Get two Starports ASAP. Build at LEAST eight wraiths, and then continue to build backups. Fully expand these badboys and you are unstoppable. I like to sweep in with a force of eight cloaked. When you use the wraiths, keep them tight and be on the lookout for detectors. Concentrate firepower on those one at a time until you can get through to a base. A lot of people put Rocket Launchers/Bunkers on the edge of a base and if you can get past them into the interior it's rendered helpless...

Ground/Air Combination:

Move 3 Siege Tanks, 2 Goliaths, an SCV, and as many wraiths as you can to the outer edge of an enemy base. If you have a science vehicle move it with them. This will allow you to detect hidden units. A sloppy strike can be eliminated in minutes if the opponent sends out cloaked wraiths. (Tanks are slow!) If you are in trouble and don't have a science vehicle, you can use your ComSat station (add-on to base) to "sweep" an area. Everything on-screen is revealed. Sweep your troops if you suspect hidden units.

Once you are in position, move the tanks just enough to wipe out the enemy detectors. They have longer range than a bunker so don't worry. Just be sure to tell your troops to HOLD their position. A common tactic while on defense is to send 1 wraith out to the attackers and lure them into your base to be wiped out by your defenses. Your wraiths are there for backup and intimidation. The tanks should do the dirty work until the defenses are gone.

What To Eliminate First:

I would suggest you obviously get rid of the defenses. Then take out the SCV's as soon as possible. Without these they cannot gather resources. Then I would take out Starport, Heavy Machine Shop, Barracks, or any other production force. If it's a human player you are up against, wipe out the main base ASAP. Some will say "go for the supply depot's" but if you have eliminated the majority of their troops it won't make a difference unless you destroy ALL the depots and by then they could have more troops built.

Base Defense:

Bunkers to start with. Fill them with 3 Marines and 1 Firebat. Don't rely on choke points unless it's close to your base. Initially you should build defenses close to your resources/base. I like using the vultures behind the bunkers. They do good damage and have a decent range. line 3 or 4 of these up and you are set. If you can lay mines, set those up along logical paths to your base. Not only will they blow up approaching units, they will allow you to monitor that area. (no fog of war!)

When things start to heat up and you get more cash... Place a few Siege tanks behind your bunkers, and surround your base with Rocket Launchers. This is a MUST. Basically think of your defense as your offense...

Expansion:

With Terrans you have a major advantage over the other races being that you can up and move your base if you are attacked. So here is what Mr. Rad! does...

As soon as I can, I move out an SCV to a new and preferably more secure location. I don't build major defenses around the first base (maybe one bunker?)... The 2nd base is the secure one. Don't use any of the resources from the 2nd base just yet, instead build up your defenses and structures while the original base pulls the resources. If they attack the 1st base be SURE not to lead them to the new one. Instead move your SCV's to a new location.

The advantage to having this second base is that you will have more resources in the long battle and you have got the option to expand the first one if you see fit.