You don't need much base defense. Try getting by without building any bunkers, and just defending early with the marines that you build, and later with tanks. You'll definitely need a good wall-off and units correctly positioned on the cliff to do damage to the zerg as the come around the corner. You can afford to expand pretty late (you only need it for the gas), once you have the majority of your tanks sieged on your cliff. Expanding late will allow you to not have to spend any extra money on base defense.
You should not stop producing SCVs for a very long time. It should be at least 10 minutes where your command center is NEVER idle. Get an orbital command as soon as your first barracks finishes, and use MULEs every time its up. Pump marines non-stop from your first barracks (no add-on). As gas allows, get your factory up and pump tanks until you hit 8. Get siege when you have enough gas to research it without stopping tank production. As your 1-base economy starts to peak, you will have enough extra minerals that you can't spend with your limited number of production buildings. At this point, build a second barracks and you'll soon be at 30 marines. Once at 30, put tech labs on your barracks and get ghosts as gas allows. You should also have extra minerals, since 2-rax marine, SCVs, and a factory should not be spending it all. When you have 400, build a command center inside your base (you'll float it down when its done). Move SCVs down from your main, and prioritize gas. You should be close to 8 tanks by now, so put all your gas into ghosts. If you can't spend all your gas on 2 rax ghosts, get more.
I got gold on this challenge on my first try. It shouldn't be too difficult if you follow good macro fundamentals (constant production, don't supply block yourself, correctly prioritize your resources).
It sounds like you're building a large army and using it to gain map control, but then are falling prey to things like drops and backdooring.
If you have map control your first thought should never be: Crush my opponent, as you're essentially sacrificing an advantage (map control) for an unsure victory (because he doesn't control the map doesn't mean he can't take you). Instead your thought should be: take the map. I think you'll find this change in philosophy will lead to situations where you have a much more powerful economy than him and you're able to kill him with attrition.
Now if you're falling prey to things like BD here is a quick check list for you:
- Are you scouting? an Observer should be the first thing you build out of Robo. If you don't go Robo, a Hallucination works just as well. Sometimes scouting means sacrificing some Zealots in a pointless charge to just get inside his base.
- If you're scouting, are you seeing it coming? Overlords on the edge of your base, Starport with Reactor + 3 Rax, all of these are indicative of certain strategies you should watch out for.
- If you see it coming, how are you responding? If you have map control that means you should be able to respond quickly. Shutting down these back door attempts is often a bigger victory than a straight up conflict
- Finally, Do you have map control? If you don't have map control that means he does, and if he's beating you with map control then your problem is not "how do I deal with a base trade?" but rather, how do I regain the advantage.
Best Answer
So before I start listing strategies I'd like to talk a little bit about "Rushes." For reference a strategy which involves an All-In within 5 minutes usually is called a "Rush." In order to make as large an army as possible in a 5 minute window you're going to make some large economic (and tech) sacrifices. This leads to two major problems:
The distance between bases is sometimes called the "Rush Distance." The reason this distance can be such an issue is because it gives your opponent time to prepare. Since a rush isn't going to be a extremely large force, this time can sometimes be enough for your opponent to build up a similar force.
That said, I don't want to discourage you from putting early pressure on an opponent, as it can often lead to a sufficient advantage and allow you to set the pace of the match. To that end here are a couple early pressure strategies which should not leave you at too much of a disadvantage:
Protoss
The classic 2 Gate rush is an example of an early rush strategy which doesn't make too many sacrifices to place early pressure on the enemy. A two gate strategy is designed around gateways on 12 and 14 (probes) before adding on a second Pylon. This means you can Chrono Boost out 5 Zealots very easily. Its easy to underestimate the strength of a Zealot because its a Tier 1 unit, but your average Zealot has 150 combined HP/Shield, 1 armor and can 3 shot a Zergling. It is a very strong early unit.
The real strength of a 2 Gate (as opposed to rushing a Gateway on 10 probes) is that it transitions nicely into an early expansion (as you should have map control with your Zealots) or a 4 Gate or 3 Gate/Robo strategy. This means you can make a significant dent in your opponent's early economy without hurting your own too much. This should give you a nice advantage in the mid game (or even if your early push fails). This is not an All-In strategy which, if it fails, will spell game over for you.
Terran
Strangely building as large a force as possible is not the most powerful force an early Terran player can muster. Instead, building strong early game units and backing them up with Bunker play is far more powerful and effective. Additionally, it has the benefit of being able to salvage the bunkers later if necessary. In this category there are a number of good builds based around Baracks+Techlab into Early Marauders (or even Marines) + Bunker.
Your biggest weakness with this early play is going to be losing out on SCV production. Start with 12 Barracks, 13 Gas, this will give you the basics for your early Techlab. Keep those 3 SCVs on gas if you want to go Reapers or Marauders. If you're looking for more Marine based play, skip the Gas and get a second Barracks. You should be getting OC on 15-16, don't use the MULE. Since you're putting together an early rush, you'll get more Minerals out of boosting a supply depot. While a MULE is more minerals in the long run, upgrading a supply depot saves you 100 Minerals right away and an additional 60 that constitute the SCVs mining time.
When you do move out (usually with your first Marauder or 3 Marines), bring at least 1 SCV. You'll use these to build/repair bunkers. NOTE: currently you can repair a bunker from inside of it with an SCV. Its unclear if this is intended or will be patched later. There are a couple ways to use offensive bunkers. You can either try to slip them in while distracting with a Reaper, you can place them at the natural (to give you early map control), or you can place them at the entrance to his main (which will allow you to advance). There are a couple things you need to worry about:
The nice things about this rush is that it transitions nicely into 3 Rax (or 5 Rax Reapers) and if it fails you can easily salvage your bunkers.
Zerg
There are a couple of rush strategies for Zerg, but many of them suffer from Zerg's weakness to choke points. That said, I've won many a game with early speedling pressure. Standard speedling play usually means 13/14 pool, 13/14 gas, 16 Queen. This means that Zergling Speed will finish right at the same time your first round of Larva spawn. As a result you can put out a large number of very fast Zerglings before your opponent has a chance to establish a standard build. This suffers from the fact that a wall can easily break a Zergling advance. Try to slip in if you can, if you can't target pylons and supply depots as they have the fewest hit points.
Alternately you can skip Zergling speed and build a Roach Warren on 18. This should allow you to push out 5 Roaches quickly. Similar to a 2 Gate build, these early Roaches are very powerful. After building your Roaches, you can either get Zergling Speed or power more drones. If you're just looking for early pressure, the drones are a good decision, if you're looking for a stronger push, the Zergling speed should allow Zerglings to quickly reinforce your roaches. In either case you want to expand fairly quickly or you won't be able to keep up with unit production. Additionally, the expansion will allow you to transition into mid-game easily, and leave you in a strong position.