Dtgreene has the right of it; that party doesn't work until MM8. Also, it is missing a cleric and necromancer, both of whom provide massive quality of life benefits.

You're right, I was thinking of 8.

I deliberated heavily on which party to use for my first MM7 playthrough which I am still on. I went with Goblin Knight/Goblin Thief/Dwarf Cleric/Elf Sor since this gave the group the most versatility. We soon learned how important melee was after getting some very spiffy early game gear that made early game offensive spells and archery (nearly) obsolete.

Skills and ranks are more important than equipment, though. With proper melee choices, you can turn your party into a lawn mower in the second half of the game – you'll be able to charge into a group of enemies in the real-time mode and destroy them all simply by mashing spacebar. Or, if you prefer magic, you can fly high above your enemies while raining down a meteor shower on them. The gameplay mechanics make level progression really satisfying.

Don't diss archery, though. It's very important in the first half of the game for taking out a horde of weaker enemies without risking injury. Or kiting tough enemies you're having trouble with using your usual tactics. Just be sure to give everyone a rudimentary bow skill and a missile weapon so that you can fire off volleys of arrows/bolts from afar.

This is what I used as well.

Thief-Cleric-Druid-Sorcerer

I was impressed by how good my thief became at fighting after promotions and bumping up might and endurance with barrels.

The least-valuable member of my group, even though I liked him, was the druid. Master-level alchemy is good enough - you don't really need Grandmaster in that. If I did it over again, I'd probably swap out druid for paladin or maybe archer. Or maybe I'd go with only three characters.

Thief - Cleric - Sorcerer

Isn't there a default party? First time, isn't the challenge to complete the game with that?

They provide a default party so people don't have to muck about with character creation if they don't want to.

Your experiences thus far sound about normal. To conserve spell points, you can have your sorcerer just finish off enemies that have a few hp left, letting your stronger melee combatants use their higher damage range on less injured monsters. Check the monster hp and use one of the cheap auto-hit spells like poison spray or fire bolt.

Two comments: 1) Stealing will never be very good, and I suggest that you stop investing in it. 2) Disarm Trap is, sadly, one of those skills that has a hard time demonstrating its worth; if it works, you'll never know how much damage it prevented you from taking, and if it doesn't then it becomes "why am I investing in this useless skill?" Be aware that only the active character's Disarm Trap is used to try and disarm a trap on a chest, so only ever invest in the skill with one character, and have that character selected before opening any chest.

So far, the Cleric has been the only one to invest skill points in anything besides Learning and Merchant. (She has 6 Body Magic ranks.) This happened because I was tired of having party healing take so long.

I was waiting for the right time to invest skill points in other skills for other characters - after quickly skilling up Merchant for the Cleric, preferably to Grandmaster, so she can buy and sell stuff at much more favorable prices.

I strongly suggest that you go ahead and select which skills each character will be using, and start putting in the skill points. It makes life a lot easier, and your sorcerer especially will never amount to much without skill points.

Other suggestions:
-Only have your cleric invest any skill points in Merchant, and have the cleric do all of your buying and selling. Other people can hold items if you like, then just give them to the cleric when you want to sell the items. Training costs aren't a problem if you do a reasonable job of looting the dungeons that you explore, so save the skill points to invest in other skills.

-I strongly suggest only investing enough skill points in learning to earn the E/M/GM upgrades, if that. When I'm playing, I just buy the skill and let it be. Especially if you can't get the E/M/GM bonuses, it just isn't worth skill points that could go toward weapon/magic skills for killing things faster.

-Note the general break points for achieving Expert, Master, and Grand Master in skills! In general, Expert needs 4, Master needs 7, and GM needs 10 with maybe some extra requirement (minimum level of Personality for GM Merchant, for example).

-Your cleric won't be able to GM Merchant until after you've gone either Light or Dark, so don't hold your breath waiting. There is a lot of game to get through before you get there.

If you'd like particular skill focus suggestions for each character, feel free to ask.

Does reaching Master in a skill require being a specific class rank (Sorcerer/Wizard, etc.)?

Is it generally best to rush to at least Expert rank in Learning for everyone and Master Merchant for at least our group's Cleric? What about Water Magic for our Sor for Town Portal?

In MMVI, Lloyd's Beacon was the best. But it comes pretty late in MMVII. But Town Portal is very useful in MMVII, and can come pretty earlier in the game if you concentrate on Water Master Skills and getting to Nighon.

Correct. Not every class can master or GM each skill they can learn, and most (every?) class has several that it can't even get up to Expert. For example, a Knight will never get beyond Normal skill level with Learning, and a sorcerer will never become an expert with a bow. A thief can GM Leather, but can only Master chain.

Also, (speaking from memory on this point) most classes must get at least one promotion before they can Master any skills, and usually two promotions before they can GM any of their skills. I don't remember the exact break downs, and I'm not currently on a device where it is easy to look it up.

This is my personal advice, but again, I wouldn't spend any points at all in the Learning skill. Buy it early because that first point is worth an 11% bonus, and then leave it alone because each extra level is only +1%. Do hire a Scholar, Teacher, or Instructor though, as those give you decent bonuses without spending your precious skill points. Instructor is the best for extra XP, but he takes enough of the gold you find to be a bit prohibitive in the beginning; a teacher will be fine until you start having some spare cash. A scholar gives the lowest XP bonus, but he will ID everything you find, so you don't need to invest in Id Item for awhile.

I also would probably push for Expert Merchant early, and then balance further growth there against some of the other primary cleric skills, like Body magic. Maybe get up to Expert in chain and shield early to improve recovery time. Keep in mind that a cleric never needs more than 10 points in Merchant, because GM merchant buys and sells at cost.

I always, always push for Expert Air Magic as my first priority, above pretty much everything else. Expert Wizard Eye is worth it. Getting Master Water for Town Portal is also a great investment when you can, but takes longer because you need the promotion first. Also, I seem to recall the Master Water trainer is in Mount Nighon?

Does the EXP bonus from multiple hirelings that boost EXP (Scholars, etc.) stack with itself? Does the hireling bonus to EXP stack with Learning?

Do items that boost skills stack with hireling bonuses?