Im a big fan of the 'Capture the island' missions, its what I mainly played before dayz and am recently getting back into it big time, in particular the popular Warfare BE (Benny edition). For those considering ARMA for a tenner, here's a breakdown (TLDR version at the end):
Each team (US/Russian) starts in a random position with a lightly armed APC that doubles up as a HQ and a couple of other basic vehicles to get started. Each person has a number of slots assigned to them AI units (typically about 12), essentially everyone is a squad leader. At the round start, one person is voted commander. The commander then has the power to use the HQ to build a base (which consists of defenses, fortifications and factories to produce units/vehicles), and perform upgrades (better gear, new units, more support etc). The advantage of having a mobile HQ is that it can be packed up and moved to a different part of the map to have multiple bases or simply just to hide it somewhere completely away from base (a personal favorite of mine is to stash it in a barn/warehouse to hide it from plane/heli missile lockons). However, new factories can only be sited within a few hundered meters from the HQ's current position. If the HQ gets destroyed then you can't build any new factories. The ultimate goal of the mission is to find the enemy HQ and any factories and obliterate them
Now the CTI bit - you only start out with a limited amount of money, usually enough for a few squad members and basic transport. However, once things get going, money is rolling in and the commander has made enough upgrades, you can buy anything from the arma CO/BAF/PMC universe (team dependent, ie US get M1s, Ruskies get T90s). Remember you have your AI slots so you could buy yourself a tank, fill out the positions with crew and buy another couple of AI tanks for support. Every town on the map has a main camp and outposts which are defended by resistance factions, these are all AI controlled and will only stay within the town boundaries. Once you have killed enough of them (ie, there are more friendly players than resistance) then you capture that town. It's best to completely wipe out the resistance, otherwise once you leave they could retake the town. Each town has what is called a 'supply value'; once is has captured, it will provide the team with an amount of money and supply each minute (supply is a secondary currency for the commander to build factories), proportional to its supply value - basically the bigger the town, the more money is gives. Also, once it is captured, it will spawn friendly AI that defend the town should the enemy come rolling in (just like the resistance faction).
Initially the other team is doing exactly the same thing as you - capturing resistance towns and expanding across the map. Soon you'll start coming across towns that the other team has already captured, capturing these towns not only gives you more resources, but it then deprives the enemy of their resources as well, however if you try to capture an enemy town they will be alerted and someone may can and investigate.
In the meantime usually someone on your team decides to go scouting for the enemy base, if they locate it then the fun really starts. My personal fav is getting a few players together, each grab a tank and get one of them in an attack chopper/plane. Roll up to about 1k away, call in artillery to take out as many infantry and defences as possible, then get everyone to roll in and blast away at every building in sight. If the HQ is there, then chances are that the enemy commander will panic, pack it up and try to escape with the HQ. Whilst the APC HQ is very fast and probably could evade a couple of tanks if the driver knows what he's doing, by driving it means that the choppers AT missiles will pick him up and lock on no problem, dispatching it with haste. If you get the enemy HQ, chances are you can forget capping any remaining towns, focus on wiping out any remaining buildings and scout for any secondary bases
There are many parameters that vary from server to server such as starting funds, how many AI units you can have in your squad, number of towns, town resistance/defender difficulty, number of bases at any one time etc.
The thing I like about it is that despite it being the same mission each time, each game is massively different. For example, once match we were obliterated in about 90 mins, the next one we had almost all the towns on the map after about 3 hours, but then the match turned into a 9 hour wild goose chase because the other teams commander moved the HQ all over the place (we could never find it, we would find a base, wipe it out only to find another one spring up on the other side of the map :/)
In a nutshell, CTI consists of five stages - building base, capturing AI resistance towns, wearing down enemy team by retaking towns they have captured, scouting/locating enemy base, destroying enemy base
