No offense intended to the other members, but everyone has their favorite system, so you'll get all sorts of advice on "what to buy".
But you already have the eGo-T, so you might want to try to get that working.
As mentioned, you should line up the tank so the flat sides match the flat sides of the wick plate.
The eGo tank is a complex bit of kit, for a clear hunk of plastic. There's a tank that holds the e-juice with a hole in the bottom cover to feed juice to the atty wick (in the center spike tube). Then there's the vapor channels that run from the flat sides into the mouthpiece. A fluid tank and a vapor mouthpiece are conceptually two different gizmos, but the eGo-T combines them on the same end of the atty.
You have to align the tank with the spike plate so the vapor can reach the channels to the mouthpiece.
Also, the tanks, as supplied, don't have the holes actually punched out. You can do that by pushing it onto the spike plate, but that could push the wick too far down the spike plate, resulting in leaks.
I use a nail just a little smaller than the diameter of the spike tube to punch out the feed hole on a new tank.
Then you have to make sure the tank is *completely* seated into the atty. If you can see *any* of the cylindrical part (before the bevel), then it's not all the way on, yet. Sometimes (especially with a new tank) you have to push
really hard.
If you don't have it completely seated, three things will happen: you won't get much fluid to the atty, so there's not much vapor, the vapor won't feed to the mouthpiece right, and you'll get fluid places it's not supposed to be -- in the mouthpiece, leaking from the join between the atty and battery, etc.
Yes, if you hold the unit with the mouthpiece down and the battery up, the juice will collect in the forward end of the tank, and nothing will reach the wick.
With the manual batteries, I find that holding it battery downward just comes naturally.
(Think of it as a bit of a "prison yard" smoking technique.

In VA, I can vape in non-smoking areas, but I don't want to be blatant about it --- there's a virtually Pavlovian conditioned reaction against smoking in the younger generation, and it carries over to vaping, too, for no rational reason.)
Vaping isn't *exactly* like smoking. You take longer, slower drags. It takes more force to suck from a PV than from an analog cigarette.
And, if you're using PG based liquid without a lot of added flavor chemicals, there's hardly any visible vapor.
I've been vaping 36mg unflavored PG from my eGo-T and if I draw only into my mouth, I'll see some vapor, but once I've inhaled, what I exhale is mostly invisible.
PVs don't produce smoke. What you're mostly seeing is water vapor condensed from the air and your body. It's summer, so presumably there's not enough vapor content to show up in humid ambient air.
I've been using the eGo-T (type B) system for a week, now, and the only real issues I've had were related to leaks.
(I probably should mix some thicker VG with the PG base, but I don't want to cut the nic content yet.)
I don't wash the attys all the time. I've water rinsed both attys in my kit to clean out the manufacturing residues and I've water soaked one to clean. In all cases, after getting water into the atty, I blow out the extra, dry it off, then let it air dry for 24 hours -- mostly on top of the satellite box that runs hot anyway.
With the 1000mAh batteries and 2ml (type B) tanks and attys, I find the eGo-T system to be extremely convenient. I fill the 2ml tank, put a freshly charged battery on it, and I'm good for the day.
(Unless it leaks. I think I need my old nerd pocket protector.

)
At home, I lay it down flat when I'm not vaping on it. That seems to produce fewer leaks than letting it sit in my pocket. If I leave it battery down, it tends to flood the atty, and I get leaks between the atty and the battery. If I leave it tank down, I sometimes get juice in the mouthpiece.
(Keep a bottle of water handy. If you get raw juice in your mouth, you'll really want to rince it out before it bites your tongue. And PG will dehydrate you anyway, so you'll need to drink more water than with analogs.)
I also found that I can't take a "vape break" every couple of hours. With analogs, I had to go down to the loading dock to smoke a couple of analogs every 1.5 - 2 hours. If I try taking on that much nic at a time from the PV, I get a buzz. Instead, I take a couple of hits off the PV once in a while over the course of a day.
I've only been at this for a week, so there may be other tricks I haven't learned yet, but that's what I've found, so far.
The eGo-T works well for me, but you have to be careful to fit the tank correctly, and then you have to adapt to the differences between smoking and vaping.
Hope my ramblings help.
Make sure you have the hole in the tank bottom plate, then make sure it's seated all the way with the tank aligned with the spike plate, and try it again -- battery down when you vape.
It really does deliver enough nic for a 2-3 pack a day smoker.
Eventually, you might want to try another system, but since you already have the eGo, you might as well get some use out of it.