There isn't a lot you can do to protect yourself initially but you can save the starport and science facility to the north. Use the liftoff command on each and land them within the borders of your base. The enemy has siege tanks now and they will use them. Begin training enough SCVs to gather resources as quickly as you can then set yourself to producing marines and get a machine shop attached to your factory to make some siege tanks of your own. Build bunkers at the three entrances to your base and stock them with marines (only use firebats vs. the zerg and protoss). Don't forget the enemy can build wraiths and will attack you from the air. Build some spread out missile turrets as well. Also, as you can rely on the barracks to defend your base somewhat don't let it be the end of your defense. Keep a force at home for this one since the enemy can reach out and damage your bases with the siege mode of the siege tank.

When you've got a secure base you should begin preparations to attack. You'll want a force of 12 marines, 6 goliaths (air support) and 4 siege tanks (siege mode) to begin your attack. Additionally, you should bring a science vessel along (keep it safely behind the battle front) to use the defensive matrix ability and detect cloaked ghosts/wraiths that may harass your units while they're campaigning. While your forces are building up for the assault I recommend building a couple wraiths upgraded with cloaking field and sending them to vulnerable enemy positions. Use the command center's scanner ability to find these. There are a few northeast of your base. Kill the units that may harass yours while they're on the road. When your army is completed begin your attack to the north where your wraiths have been working.

The orange confederacy base to the north shouldn't be hard to take care of. Take your siege tanks within range of the bunkers (not within THEIR attack range) and use cloaked wraiths to relay the position to the siege tanks. This is how you can attack things that are on a higher elevation. Be sure to bring your science vessel along to detect cloaked enemies. Leave the siege tanks here so they can attack any enemy units coming from the ramp to the east as this is where most reinforcements will come. Take your other ground forces to the northwest up the ramp and move them into the base. The marines can use stimpaks to deal damage quickly to the many goliaths you'll encounter here and when your science vessel reveals a cloaked wraith the six goliaths you hopefully brought with you will tear them from the sky in seconds. When this base is destroyed you may have new issues to deal with.

By 'new issues' I mean needing to find a new source of minerals. There is one to the east of your base where the siege tank was which eliminated the supply depots there. Make sure it's not still there (use some wraiths to take it out then either build a new command center or relocate your old one. I chose to build a new one as I had the resources. The old one was still a functional scanner and the vespene geyser nearby was still useful. When this is done (don't forget to set up some bunkers/missile towers near the new command center) begin pushing your troops to the east. This is the main enemy base and it will probably be the most challenging battle you've had so far.

I recommend replenishing the forces you used before for the next attack. I had minor losses (although the marines were wiped out) and, after building more marines and repairing the machines I had, I was ready to go again. It's highly likely you'll meet enemy resistance almost immediately if you march your forces from the east of your new command center but it's the best way. Deal with them while they're close by and repair with SCVs before you press further. You can keep the marines and goliaths out in front while the siege tanks go into siege mode behind them to really rack up the damage on the enemy. I said this was the hardest battle but that doesn't necessarily mean it's borderline impossible. Remember to bring that science vessel along and you shouldn't have a lot of trouble. Don't bother eradicating the entire base, just make sure all the military defenses and units are gone, then attack everything else. You can get the SCV holding the emitter to the enemy base at your leisure at that point.