Priest lvl 25 proglems regarding talents

We are group of 3 friends who exclusively play always together when we have time.
(We are now at 25lvl)
Warlock affliction
Hunter BM with bear as a pet.
And me as a priest who is completely lost with talent path for healer role. Many people say holy, others disc, some even shadow (at low levels). Ive tried holy, however it was always hard to manage mana, as I dont have gear yet. So does that mean the optimal way is to go disc? We often go dungeons, and when it comes to healing I quickly lose mana when going as holy.

Does that mean, that priest is kind of weak in terms of healing in low levels, and its better to go spriest as dps and let other classes heal?

Ive read Mercy’s in depth guide about hpriest, but unfortunately for low level scrub like me it is not revelant yet.. :(

If you are always with your friends, then there's no need to use Shadow talents. Those talents are meant for damage to help you play solo while you level up.

Your mana will be problematic early on in any case. Try to get spirit and intellect where you can. You can consider getting the Spirit Tap talents in Shadow, just for the mana regen, and stop putting points in Shadow after that.

Discipline is more mana efficient than Holy is, but at low level, it is going to make very little difference. At your level, try to use Heal instead of Flash Heal. Also try not to cast heals when you don't really need to. Use your wand to do damage, instead of spells. These things should help with your mana.

Mana is a problem for any class that uses it at low levels, unfortunately.

As you are not doing the leveling alone, remember the "Spirit tab" is only activated, if you do the killing blow on the mob. So most of the time these taent points are wasted.
I did level a number of priests in the past 15 years. Lets see how I would skill at 25:
Improved renew 3-3
Holy spec 4-5
Divine fury 5-5
Inspiration 3-3

Further take these:
Improved healing
Spirit of redemption

Try to get into Shadowfang Keep and get the Robe of Arugal. One of the best robes for starters.