When do i buy which citadelle upgrades?

IMO:

buy gold I as soon as you hit war score 3
buy building hp I early

use all other gold on items

never buy priests until war score 8 when you can get catapults as well and go for a citadel push, early game priests provide the enemy team with a tonne of extra exp and gold

only consider creep dmg + armor upgrades when you have giants, otherwise it just makes the creep waves closer to the enemy base = easier for them to retreat, and harder for you to retreat

The first gold upgrade is very nice, as it pays for itself in about 5 minutes. Higher ranks, however, aren't very good as the bonus isn't as large. Getting this early is a great way to out-gear your opponent.

The xp upgrade is great to outlevel your opponent early, especially if there is an xp flag that you can maintain control of. But I put the higher priority on the gold upgrade, as higher level items will let you defeat enemy DG even if they outlevel you. But if your enemy gets priests, then definitely go for the xp upgrade. Which actually leads to the next point:

As a rule you should generally avoid getting priests unless you have the warscore/gold to quickly upgrade to at least catapults. They give nearly twice the amount of gold and xp and are usually more of a detriment than a benefit.

Finally, there are other useful upgrades as well. The building health upgrade greatly extends the lifespan of your towers and is probably the first upgrade you should get in a fortress match, especially since it's cheap.

my rule of thumb is never buy a minion upgrade first, and if enemy bought it only buy it if you are being pummeled

or buy all when you have gold to push down to at least cat

thats what i thought so far... but i wasn´t sure.

what to do with the other updates?

Some you should ignore completely, others you might want to get late game or in certain situations.

You should ignore the death penalty upgrade because it's pretty much useless unless you're dying a lot, which means you're probably losing and should spend your gold on items to make you stronger instead of an upgrade that will let the enemy kill you faster. I've never noticed the building damage upgrade do anything so you should probably avoid that as well. The finger of god is completely useless.

The damage, health, and armor upgrades to reinforcements are good late game when you're making that final push to the enemy citadel, but otherwise there are better things to buy. Trebuchets can attack towers and other DG, but I've never found them to be that great. In the fortress game-type, however, some of the fortresses are close enough for trebuchets to hit.

First level of building damage is decent because it gives your towers AOE attacks.

i try to buy Building Health 1 almost immediately to stave off early tower losses. can help the early game EXP race alot if you can manage to keep your border towers up for a bit longer with this upgrade. 

the next one i go to buy is usually Building Damage 1. two reasons for this. first is that it grants AoE damage to tower attacks so enemy DG's won't be able to screen themselves from tower hits by standing next to minions or creeps. second, its cheap as hell. 

i'll sometimes try to get Creep Health 1. this can slow down enemy farming of your creeps and also will make your creep waves beat enemy creep waves with a little health left over so they can naturally advance the battle line up the lane a little bit. every little bit of territory helps. 

I personally like to get Experience Upgrade 1 but its not as popular as it deserves to be. often money is tight in close games so you might be forced to choose between this and Building Damage + Creep Health (similar cost, about 1100 for that vs 1200 for Exp).

Obviously Gold Income 1 is extremely important and you should get it at war rank 3 if possible.

after that you don't need many upgrades at all. most will just save up gold and wait for war rank 8 to buy the big creep push (priests, angels, and catapults all at the same time).

Once you've bought the creep push its pretty important to upgrade their health and damage so they charge to the citadel fast enough to prevent your enemy from stabilizing and farming them out. 

My general rules, and this can change depending on my opponents tactics:

1. Gold Upgrade 1. The sooner you get it, the more gold you'll have collectively across the duration of the match.
2. XP Upgrade 1. Usually, I only get this if there is an XP flag, as mentioned above. This will increase the XP gap between yourself and your opponents enough to help decide the outcome of the game.
3. Building Regen 1. If your enemies are pushing against your towers right from the start, I'll grab this first. It's usually a good idea to wait a while, as most games take about 3-4 minutes befores towers face any real dangers.
4. I avoid the Death duration decrease, as basically my intention is to not die.
5. I avoid getting the priest upgrade until my team has a clear advantage on the field, thus increasing our ability to push, or until the enemy purchases their upgrade.
6. I save the DMG and Armour upgrades for the creeps until after Giants have been purchased, or if it's clear the enemy has purchased theres. The increases are marginal at best, and really need significant numbers on the field to make a noticeable difference.

I find building damage 1 is useful if your enemies are pushing with minions (that aren't siege archers).

I don't think it's a good idea to make a set pattern... do what you think is best in your given situation.

For example, if the level of play is high (most people are good), buy gold then xp because your teammates know what they're doing and will really benefit.  Otherwise, focus more on outgearing them and upgrading towers so your teammates have a place to hide and the enemy can't make progress as easily everywhere you are not.

Couldn't have said it better, Sly.

Have people used the building damage/health upgrades above 1 much? Is it worth investing in those?

The building health upgrade is usefull when you know your towers are going to take a lot of damage at some point. I haven't had the opportunity to use the +DMG upgrade for the towers much over level two, most games don't last long enough.

I once played a 3vs3 on leviathan where it seemed like the opponents bought a lot of armor and damage to their creeps and then upgraded to priests. It was crazy. Couldnt kill more than 2 waves of creeps before my own health had almost disappeared. It really felt stupid because we were really afraid of their creeps in that game.

Has anyone else tried out this tactic?

I had an epic game once where a part of our end-strategy involved buying all death upgrades.

Every upgrade in the Citadel is useful, depending on the situation.

Just lost a game where the enemy had fully upgraded their troops - you could really feel the punishment.

about the gold update: at level I it adds +2 gold?!

i cant imagine numbers with this...

i get 2 gold per second more with this update? that sounds like a very small amount...

so if i would play 10 minutes i would get 10 (m) * 60 (s) * 2 (gold) = 1200 gold. thats not really much within 10 minutes.

or how is gold getting counted?

It gives you 4 gold per second. The second upgrade 6, the third 8.

I haven't played with it, but I've played against it (they had clearly upgraded creep damage and taken priests).  I was totally surprised by the creep damage being dished out.  I was forced back multiple times by creeps in that game, I just couldn't take the damage being dished out.  I think we ended up losing that game.

I don't know what level they had the damage at though to make it so strong.  It was particularly effective because we were playing on Leviathan and they were able to hold the Debilitating Flag.  Interesting tactic that's worth exploring.

Koz 

In a 4v4 game (on the big round 5v5 map) our team got totally owned yesterday, but we won in the end, because they team ganked all the time, but we had higher levels and we got priests at the right time, so basicly not adapting their strategy got them killed in the end.

I'd say on big maps you can get the priests earlier, especially if there is alot of team ganking (which there usually is, especially with towers=strong). The team ganking lets like atleast 2 of 4 lanes of you priests push thorugh, if you keep the enemies occupied.

keep in mind gold upgrade is active for each player on your team.

it will repay the player who bought it in approximately 450 seconds (7 mins, 30 seconds). however during that same period of time it was pure profit for every other team mate. 

Gold I - Like many wrote before, do it as soon as possible. Your team (and even you) will get more gold than paid in no time. The other upgrades are imho to expensive for that fast game. Maybe the 2nd in a 5vs5 game I would buy, when I don't need the gold for items or I got many kills (and so the most gold, too).

Tower Upgrade I's - They are cheap and give them skills they don't have before: HP regeneration and AOE. I would get them early and nearly always. The other upgrades don't help to keep towers up, because they are normally attacked by 2+ heroes or catapults, where more hp regeneration or damage doesn't help. At least with those low values. (My experience).

Death Upgrade - You should follow the number one rule: Don't die!

Creeps - Wait till you can attack the base or the enemies bought it. Damage and HP upgrades are very expensive for their low bonus, but you have to have stronger creeps than the enemies if you want to push instead of defending against creeps.