Hi!
I can help you with some things as I am also playing similary to you
Now, Cults. I've seen around this forum claims that you should strive to remove at least one, possibly two before the first year... How the hell? I found the two HQ missions I did a pain in the ass with eight people delivered by Dragonfly - and thinking about it that would have been an incentive of building a logistics base with a hagar, living quarters and storage to base an Osprey in range of where certain HQs appears. That in fact was the reason why I had to skip the first two times the Red Dawn one popped up - my Osprey couldn't get to it, and it was a suicide trying it with five people. However, I did get the Dragonfly researched and available before I could get the money for a third base so it became a moot point.
Those were people who built base near spawn of HQ and sent mudranger with crew as far as i remember
Dont try that at home
I removed 3 of 4 basic cults by the end of second year(none at the end of first) and 4th was still there only because HQ did not want to spawn.
The basic merit of more bases is more scientists which provides you with better equipment when alliens appear(also more soldiers and better ranks - I think at the end of second year I had 4 bases with 16 soldiers in each). From what I remember all my troops used Cyber Armour when aliens struck - also I think I had skyraiders/skyrangers/skymarshals then. The best one of those three do not remember which one is that right now
As for how you should replace your dead soldiers or lose less important ones for that matter use HWP and dogs - they are godsend as you can just produce/buy more! But basically as soon as you get sensible HWP you should send as many as you can in your ships. They make excellent scouts!
As for weapons - every single person that plays this mod has it`s favourites and say that rest is useless
but it seems that every one says that about different weapons.
Miniguns are great for removing bigger number of enemies(great for those cult of apocalypse missions where there are millions of targets)
Sniper rifles dmg depends on accuracy of your guy so they are great in capable hands
And so on - I would suggest looking at Starving Poet Lets Play as he is literally testing every weapon he finds so you can learn a thing or two.
Hope this helps
But you were very unlucky to get sectoid base attack - anything nonpsionic would be easier - I only got a lot of Syndicate attacks, floaters and mutons to attack me so it was much easier...