For PvE you will mainly be in DPS majority of the instances don't require you to be in a specific defensive build, also aggro is mostly based on DPS and you aggro skills only support that if you have a very heavy DPS in your group he might take aggro from you sometimes if you are doing no damage. Keep in mind DPS doesn't mean greatsword only as you said you need to play with both gs and s&s and switch accordingly (as example you have an aoe taunt that makes you block one attack 100% so when you know a big physical attack coming you do it and then you can also use a skill that gives you a big buff = courageous shield and go back to gs and repeat to refresh it).
Your first PvE gear will probably be also your first PvP gear that is BM gear (which is also gonna be your main PvP Block set later) then you can either try getting in groups for easier late game instances to get some pieces or farm ancient coins. Ancient coin gs fused with BM gs will be your friend for a long time as a good starting weapon for everything. I go for the armor as well since it's easy to max that gear at +5 and gives very good stats but gonna take a while to complete. For s&s you can keep your BM ones but try to replace them for PvE with drops from instances you don't have to farm ancient coin ones.
For pure DPS I go with this : http://aion.aspirine.su/stigma/#dCnagacfmdiaBcaBeabgsgfahgBddBfe you can replace Siegebreaker with Bodyguard for your party members or one of the taunt skills if you want an extra insurance.
Only special cases instances is DLR if you find a premade to run it for the extend you will need a magic resist set, either the kahrun or rune shield tower might be good and ofc you will need the tank branch in your stigma tree but you shouldn't bother with this that early.
For PvP for Templar to be optimal you will need multiple sets later like cleric and chanter. Your first PvP gear that is BM gear will be your Block set against physical classes, against magical classes you have 2 options, either Magic Resist or Magic Suppression. For Magic Resist the best is to go hybrid on damage and MR with the abyssal gear (star 2) some prefer to make it full dps and go ham on damage vs all classes so that's your choice on that. Magic Suppression your best bet to be also doing a bit of damage is the Ancient Coin leather gear coupled with a sword and shield with the most ancient manastone slots possible like rune shield tower (cause you need to slot magic suppression stones). So when farming ancient coins you can go for this instead of plate armor for PvE if you'd like, you will also need a hat with the highest suppression possible like the crafted ones or sunayaka (also good for magic resist). If you want you can have a hybrid magic resist and suppression set (if you are planning to make your abyssal full dps) but only used as a defensive set then maybe the cloth ancient coin is better. Use the gear builder to plan ahead and look for the stats you need : http://aion.aspirine.su/ *you will also need to make macros for gear switching.
As for stigmas for PvP here where you have some choices, Divine and Empyrean Fury are a must so there goes 6 slots. You need your pulls so there goes 2 more. Unwavering Devotion is a must. You are left with 3 slots to either get more damage skills, Inquisitor's Blow is useful as it's a ranged skill that you can also use to remove dodges so you can pull them after or get lucky and get a KD from a crit, your other DPS skills are Punishing Trust your biggest burst skill and Punishment that have some randomness to it so meh. Stubborn Spirit is really nice stance (either when you are chasing or escaping or to reduce damage from magic nukes) and is a must to complete your magic suppression set but still useful without it for what it gives, Aether Armor for a big MR buff vs magical classes or to couple it with your magic resist set or even without it if you want. Barricade of Steel is in a weird spot where it's very good vs assassin and gives lots of block, the reflect damage is bigger than your Holy Shield but it's debatable if it's useful overall to take up a slot, generally you will want a "static" do it all build in open PvP that gonna be useful against the majority and especially magical classes that are annoying for you (and you won't be back and forth switching all your stigmas). Last is Bodyguard if you are doing group pvp or with a duo friend.