If you're not min-maxing at the level cap, your best bet will generally be at least one, if not two, of the three Gathering professions, Skinning, Mining, and Herbalism. If you do decide to take a crafting profession, choose the gathering profession that meshes most closely with it (i.e., if you take Leatherworking, grab Skinning, Engineering, grab Mining, or Alchemy or Inscription, take Herbalism.)
If you want to make money using a crafting profession, the best choice before the cap will be Inscription, as the Glyphs you can produce as early as level 5 will be used even by level 80 characters, providing you with a constant market.
If you want to produce things you yourself will use on a regular basis, Engineering provides fun toys, and trinkets at much lower levels than they'll be availiable as drops. Leatherworking allows you to make your own armor, but drops and quest rewards will, for the most part, be better than what you can craft - at least until the Cataclysm expansion releases. Alchemy will allow you to make a variety of useful consumables, but in general, you will have to make many more than you'll be able to use as you level, and there won't be much of a market for what you craft.
Enchanting is a viable option as well, and you'll be able to enchant your own gear as you level, which is handy.
Realistically, until the +Stat bonuses at 400+ skill come into play, there really isn't a 'best' or 'most useful' profession. There are a few that will be much less useful to you as a hunter, such as Blacksmithing and Tailoring, but for the most part, you should be fine picking out whatever you find fun.
The only other major note worth making is that each of the three gathering professions provides a free 'passive' boost as well. Mining will give you some extra Stamina for free, Skinning will give your character increased critical strike chance, and Herbalism will teach you Lifeblood, a free Heal-Over-Time spell you can cast on yourself on a short cooldown. The crit from Skinning especially should be very handy for a low level hunter, though the other two perks are nothing to sneeze at either.
You're right in that you should not have tried to heal as Enhancement. Not only are there equipment differences (I'm guessing you didn't have much INT or spell power gear?), but by not being Restoration, you miss out on a powerful heal spell (Earth Shield) and a 1 second cast-time reduction on your only other healing spell for that level - Healing Wave.
As soon as you hit level 30 (At least, I think it's 30...) you will unlock the ability to have a dual talent spec. This means you can have a restoration spec for healing instances, and an enhancement spec for soloing when you're not running dungeons.
Regarding being kicked from the instance group: it's rough being a new player, and sometimes other players forget that. Chin up, don't let it get to you, and I'd suggest finding a guild, or making some in-game friends that can help you learn.
Best Answer
In terms of classes, trying to cover all three roles between the two of you is a good target. When you guys are questing together by yourselves, having one person be DPS and the other healing helps keeps downtime to a minimum. And if you guys decide to use the Dungeon Finder, having one person able to heal and the other be able to tank ensures you'll never have to wait long in the queue.
Blizzard has homogenized the classes over the years so there is a tremendous amount of overlap between the classes and specs. As long as you guys cover the three class roles, feel free to choose whatever fancies you.
For reference the hybrid classes are:
If you're going to take my advice about role coverage, you'll want to avoid Mages, Hunters, Warlocks, and Rogues as they can only be one role: DPS.
Since you're talking 1-85 play, Death Knights are off the table as they start at level 55.
Putting it all together:
In terms of professions, I'd avoid the heavy crafting professions that take a lot of time to level up and are usually taken for the Bind-on-pickup endgame recipes: Blacksmithing, Tailoring, Engineering, Leatherworking. Instead, focus on the professions that'll let you help each other out while leveling, like Enchanting and Alchemy, or the gathering professions, like Mining and Skinning, which will prove lucrative and won't require too much (if any) time soloing.