People m,ore familiar with BG1 might want to add to this.
NPCs who fight
BG1: Jaheira and Khalid, Xzar and Montaron; Minsc and Dynaheir, Edwin; on the think so but not sure count the two dwarves will probably fight as will Shar-Teel and Eldoth.
BG2: Viconia and Keldorn; Minsc and Edwin; Aerie and Korgan; under the right circumstances Anomen and Keldorn/Aerie. Anomen will also attack the PC if you play your cards right/wrong and then tell him off for having a hissy fit over it.
In terms of stats, the only thing to watch for is that if any stat goes to 0 it's insta-death for you. There are enemies that can drain stats, though stat-boosting potions will help avoid death through stat-drain. Intelligence is the main one to watch here - as a side note, did you know undead cannot have their brains eaten?
General advice
Save often, and keep a backup save at the start of quests.
The default AI is rubbish, for battles you're better off turning it off and managing everything personally.
Use the TAB button to highlight usable objects. You'll miss a lot of loot if you don't.
Try and take out enemy spellcasters first. Arrows will interrupt their spells unless they have protections up, and elemental damage will go through some of the more common protections to boot. Poison is nice too.
On a related note, in BG2 there's a particularly nasty type of golem, which fortunately is stupidly big. This means they get stuck in doorways, and while supposedly only blunt weapons can damage them, ranged weapons with elemental damage will also work.
Most NPCs have a particular quest or two associated with them, so in BG2 at least it's better to have a 4 or 5-person core party and take the others on a rotating basis. This is harder in BG1 since they often come in 'til-death-do-us-part pairs.
In terms of balanced party composition, you want at least one mage, one cleric/druid, one thief, and one fighter. For BG2 a multi-class thief is more than sufficient. Ideally you want a backup mage and divine caster, and at least 3 capable fighters - multiclasses are great for this. You don't need more than one thief.
If you're comfortable with cheese, thief traps are the bomb.
Multi-class thieves can only backstab with thief-capable weapons. It's generally agreed that the best backstabbing weapon is a magic quarterstaff you can get in SoA/ToB.
Use the right tools for the job. Many weapons are only intended to be truly effective against a single kind of foe, but are really effective against said type.
When starting out BG1, you're weak as a kitten and ranged weapons are your friend. By mid-late BG2 you're pretty tough and melee or magic is the way to go, unless you're playing an Archer. If you're going an archer, shortbows are generally the better option unless you have a serious role-playing preference for longbows like me.
Likewise, most Paladin PCs seem to be 2-Handed-Sword users in BG2 at least (hint hint). If you want to go the sword-and-shield route, longswords, bastard swords, and maces or warhammers are a good option for stuffy-pants knights. If you are playing a Paladin and you choose the Cavalier kit, they can use magic throwing axes despite not being allowed ranged weapons.
If you can't handle a group encounter, try luring the enemies away one or two at a time, or using the environment to create bottlenecks. If you have an invisible character blocking a door foes won't be able to pass it and your ranged characters can thin the herd.
If your PC is a mage, don't choose Magic Missile or Chromatic Orb for your first spell.
Try Sleep or Blindness instead.
If you are going a pure-class mage, consider being human and taking a few levels of thief or fighter first then dual-classing to mage. The expanded weapons options, damage and attack bonuses, and extra hitpoints are well worth it. Fan favourites include the level 13 kensai/mage, though that requires a reasonable grasp of the spell system, or the berserker/mage for the sweet immunities from the rage.
On a related note, while Fireball et al are pretty cool and fun to throw around, mages are actually more useful for controlling the battlefield with spells like Confusion and Slow (and summons) than at causing direct damage. Casting a single Confusion spell and letting your fighters clear up a group of ineffectual foes is way more effective than blasting everything with lightning bolts. The magic system is pretty involved which is why I recommend more than one playthrough, but if you only do one just read the spell descriptions and experiment.
If your mage's intelligence is too low to learn a spell (i.e. s/he too many spells already etc) have her/him drink an INT-boosting potion and try it then.
Mages/bards can wear elven chain without spell-casting failure, and thieves can wear elven chain and still use their thief abilities.
Use the BG1 stat-boosting tomes on your PC - the stat boosts for anyone other than your main character don't carry over into BG2, and most of the BG1 NPCs don't show up as playable characters anyway.
Over 100% resistance to something actually boosts your health when you get hit by that effect. This is really useful insta-healing in elemental-themed dungeons/puzzles.
Pre-battle buffing is your friend.
Pick-pocketing is a surprisingly underrated skill. Most of the time you get bugger-all but sometimes people carry some really useful and/or valuable stuff.
After level 20 Clerics using Turn Undead are the ultimate lich-killers - TU ignores magic resistance and spell protections.
It may seem minor, but your choice of party formation and portrait order can actually make quite a difference.
If your PC has low Charisma, don't fret too much - there's a ring that boosts it in one of the first mini-dungeons in BG2, and a heap of CHA-boosting items as well. Also, the game only uses the CHA of the lead portrait, so you can make an NPC with higher CHA your party leader and leech off their beauty instead. The higher your Charisma the better your prices in stores, so it is worth decking out your lead in CHA-boosting gear before major shopping trips.
If you have a character dual-wielding, you only get 1 attack per round with your offhand weapon even if hasted, so when choosing an offhand weapon look for weapons that give you decent effects while equipped rather than good damage or on-hit abilities.
Similar principle applies for shields - look for shields with good extra effects rather than just a good AC boost.
Keep the Pantaloons.
Don't bother with the BG2 romance if you're playing a female PC - Anomen's a douche and the Haer'Dalis romance got canned.
