So you want to play through the Legacy of the Void campaign story but you're not incredibly good at playing it and it's starting to get a bit frustrating? Here's some tips. (Comments are welcome!)
Your best offense is a good defense
The method that's usually recommended and that's worked for me on my first playthroughs of any of the Starcraft campaigns is to simply build up my base and make a strong defense, and later move my army across the map and crush everything in my way.
Pros: you're sure to always win.
Cons: it takes a long time to do every single map.
Your first few minutes are critical
Yes, you have a lot to micromanage in your first 2-3 minutes of each game, but making sure you're starting right will ensure that you're not running out of resources and don't ever have to worry about that for the rest of the game.
Build 2 probes - they will automatically go on to mining minerals.
Build 1 other probe - make it build an assimilator to start extracting vespene gas.
Then for every following probe you make, go 1 to the assimilator, 1 to mining.
I'd say the maximum recommended probes that are assigned to your base should be 12 or 13.
But make sure you don't blow immediately all your resources on probe-building - you'll have other things to worry about.
Scout for close resources
Meanwhile, take 1 unit of your starting fighting force and have him scout around your base to look for extra mining carts and vespene gas that the devs kindly left lying around to help you boost your production. That's the developers' way of rewarding you for not being holed up in your base all the time.
And make sure to check everywhere around your base - sometimes the devs have been sneaky and have left some hidden right behind you where you'd assume there would be nothing.
Prepare for battle
Check your base's assault points
At this point, in between building probes, you'll have some extra minerals stocked up.
Time to build your defense. Look at your base and figure out all the possible assault points to your base and know that the computer AI WILL attack you from all the assault points. It's not a maybe - it's a definite will happen.
So how do you prepare for that? You build photon cannons. And in order to use the cannons, you need to build additional pylons.
Build your pylons and cannons
Set your pylon a little bit further back from the choke point you're going to cover, and put your cannons on each side of the pylon. Then when those are built, add cannons to protect the other cannons. This is the tricky part and you'll figure this out by playing the game enough. You'll probably have enemies that will come melee your cannons, so it's good to have other cannons in range that will help pick off those enemies while they're busy attacking the one cannon.
Build a Shield Battery
This is great! It'll recharge the shields of your constructions and minions. This extends everything's life in your base. If you've done your pylon and cannon placement correctly, dropping one of these immediately behind the pylon should be covering your whole defense setup.
Build your army
Depending on the mission, you should already have 1 or 2 buildings up that can start creating your army. Have them always working on making a unit (right after you've got your probes working on gathering your resources).
A good tip here is to set a rally point. When you select your building, in the building menu you'll see an icon arrow. Click this and you'll be able to select where your mobs will automatically go when they pop out on the map. Of course, the logical places would be to stand near your cannons so they can help out when you're being attacked.
Make and protect your anti-air units
I am not telling you what you should add in your army because there's no good way to proceed. But I'll recommend that you make sure you're covered for ground and air attacks. Because the moment you'll be able to produce anti-air units, the AI will send you some air units that can attack ground units. Try to strike a balance between anti-air units and ground units, because anti-air units usually have a weakness that the AI will exploit, so make sure you're covered in that respect.
Feel the flow
I know this is a lot to cover for a simple base building strategy that takes about 7 to 10 minutes, but you need to have a plan of things to do to make sure your base is secure. And ultimately, it's up to you to figure out what's the best thing to do in the given situation you're in. Don't forget that campaign scenarios don't always start with the same units and buildings, and some scenarios also have timed objectives. So you have to figure out how to get comfortable enough to soldier on and beat the game.
Yes, you'll end up with an incredibly strong base against an AI you'll crush like it was nothing, but hey you'll have beat the campaign and got all the story, right?