The key is to pick them up when damaged and drop them behind the undamaged ones, we are ‘jerking off to them’ because tanks, and later Goliaths are simply better than wraiths. Not to mention easier to keep alive, Wraiths are very vulnerable to aoe.
Doesn’t matter that sci vessels can’t teleport, you would want to keep them with your Goliaths anyway.
And you can always get the Armory healing upgrade if you use them away from your Goliaths a lot.
And go for the Immortality protocol mastery, it offsets much of the cost of losing tanks, though you should work on not losing them at all. 
And yes you should get vespene harvester asap, since it’s basically an extra worker you can insta build to make your ramp-up faster, which is why you should go with that mastery until you’ve become better at playing Swann.
Use Combat Drop to tank damage if you struggle keeping tanks alive otherwise, you can push more agressively at the 8 minute mark, or before that if your ally can tank for you. If there are too many enemy units, just pick up the tanks and drop them a little farther back.
The 4:00 drop should have cleared the first wave and been sent to the objective/contested expo.
Again, watch a few vods and replays, I’ve already mentioned some, to see how it’s done.
And work on the list of problems, I’ve mentioned.
Don’t play on one base, even if it seems easier, it will give you a worse economy and mean you can’t afford losing units nearly as much. The timings are also fairly different compared to a fast expand which I think is more important to learn.
Learning to pull off a fast expand fluidly is pretty essential to learn, so practice on something like Void Thrashing as I’ve said, and in a few days, show how you’ve improved (hopefully)
You can also play on a custom coop map if you just want to practice the opener, play the first few minutes multiple times and restart every time you make a mistake in your build.
Just go into the arcade and search for Void Thrashing etc.
