I think I would go with you initial thought. An Archer Cleric looks a good option. Core rule book contains everything you need, and you will be a useful/powerful character. On top of this he/she could be fun to play. Personally I like clerics and enjoy playing them.
With any class with know all the spells on there spell list I always pick up Scribe scroll at some point. It is possible to just leave slots open and prepare the utility spell you just found you need, but I prefer to make scrolls
Considering the fact nobody in the party can heal for $#!t, Cleric is the only real option. I'd go Desna for luck and travel and shoot with the crossbow
Considering you are stuck with those stats and you can't re-array them around, the Cleric is your best bet.
Your party is really good in terms of offensive capabilities, and any skills your party needs, the Sorcerer and Rogue have covered. Anything they are missing on, the Cleric can help/vouch for.
The only lacking part about this party is healing, buffing, and recuperation. And the Cleric does a great job at this.
Another possible means of support could be with a Druid as well, given their casting statistic is also Wisdom.
Keep in mind that as a Cleric, you might want to increase your Charisma modifier with your channeling capabilities, as well as the Selective Channeling feat, so you don't end up healing the bad guys with your channeling.
What about bumping Str and going with a reach weapon? This allows you to support the tank in multiple ways by being 5' to the side and back. You are in range for heals, you threaten, you can aid another for ATK or DEF, etc. If you go with something with trip you add an additional element, throw in combat expertise and improved trip not only do you get the trip benefit but can squeak in another point to AC as needed. Just my 2 copper pennies.
So we started and everything is going well but now I have another question. I only get 2 skills per level. Do I want to invest in the same skills over and over or spread them out? I've never really played a higher level character since I'm new to pathfinder and I am not sure if should be pointing my skill points in same 3-4 skills each level or if I want to put points into a little bit of everything.
One of the biggest problems dumping Intelligence is that you lack majorly in the Skills department. Trying to be both the Face and the Combat Cleric is a very taxing job, and with a dumped int, is sure to be challenging without items to help.
Maxing out your 2 Skills (I'd assume Knowledge [Religion] and Heal are the skills you're taking) is going to be your best bet, since the only other method of obtaining skills is by increasing your Intelligence via Headbands, due that it is a Core-Only Game. Anything your character can't cover for, the Intelligence Headbands most certainly can.
If you had 3 or more Skill Points, I'd say keep that extra Skill Point as your "divvying" up between the less required skills, such as Climb/Swim. But such is the sacrifice of lowering Intelligence for a class that is somewhat dependant on it.
I would either max out 2 skills that benefit from a good check, maybe diplomacy and sense motive, or play a bard instead.
A bard could still be an archer and while you won't be any good at healing in combat, out of combat with a wand of cure light wounds you can do the job. You get a whole bunch of skill points and bards have lots of good powers.
Clerics are a good choice too, but it really depends on what you want to focus on, clerics get more powerful spells and channeling, but bards are crazy skilled and inspire courage will be insane with your party setup
You won't be inspiring anyone if the whole party is dead...
I would either max out 2 skills that benefit from a good check, maybe diplomacy and sense motive, or play a bard instead.
A bard could still be an archer and while you won't be any good at healing in combat, out of combat with a wand of cure light wounds you can do the job. You get a whole bunch of skill points and bards have lots of good powers.
Clerics are a good choice too, but it really depends on what you want to focus on, clerics get more powerful spells and channeling, but bards are crazy skilled and inspire courage will be insane with your party setup
I think Atarlost said it best up above: Clerics fill a needed role beyond simply Cure spells. Between Lesser Restoration, Raise Dead, Heal (to name a few), you won't be able to cover all the bases unless you went full divine caster.
You won't be inspiring anyone if the whole party is dead...
Some could argue that the best defense is a good offense... but I digress.
At OP: Archer Cleric! Archer Cleric! Archer Cleric! Do it! I was thinking of something along the same lines myself, but I wouldn't go Community or Animal domain. I'd argue Law is a better domain, with the ability to guarantee that 11 roll every time you need it. Animal gives you control over animals (blegh!) and eventually an animal companion (3 levels too late...), so if I had to trade away one domain, it'd be that. Unfortunately, since you mentioned being limited to Core-only, that restricts access to great sub-domains like Feather and Growth :-/ so Community may not be that bad.
I'd say that Craft Wands is better than Scribe Scroll in the long run though I'll echo the sentiment that maybe somebody else should pay that feat tax if you're trying to focus on archery.
Since your animal companion will be a little weak (-3 levels) maybe it could serve better as a mount than going directly into melee. Being able to move around and still cast spells or full attack with your bow can be nice.
Spiritual Weapon and Summon Monster spells can be nice for a healer since they give you a way to make attacks even when you spend your turn buffing or healing people.