Against the different boss, heavy healing is necessary. Starting with the third or so boss, he will hit twice per round, often with multiple target spells (megastorm or something like that in english, for example), so heavy healing is needed. Plus, some can heal themselves, drawing the battle in length. A dedicated healer is, in my humble opinion, necessary. Even with a priest dedicated to healing, I am sometimes constrained to use the healing spells of the main character to keep the whole group alive.
Unless you manage to have a damage output of hundreds of damage per round, you won't be able to kill a boss before he kills you.
Edit : Sometimes use of buffs/debuffs is mandatory. You won't survive a heavy hit with an alteration on your party and you won't damage a boss with protection on him, thus, you must counter those spell with the appropriate buffs/debuffs, and a buffing/debuffing player does not deal damages. Likewise, you have to counter alterations effects (sleep, paralyze, etc.). Also, the time a member of your party is healing himself or another one, he doesn't do damages. Having completed DQ4 and 5, and seeing DQ9 is the same and even harder, I can tell you cannot survive without proper healing.
The healer is quite useless on random monsters encountered on the map. My personal advice : specialize your healer in magic wands, this way you can regen the MP of your healer on the random encounters to arrive fully charged against the boss.
Your bag can only hold 99 of each thing, for both equipment and consumable items. If you have fewer than 99 of something, you can buy up to 99, but not above.
My strategy is to periodically sell down my inventory to one of each standard equipment and 50 or less of replenish able consumable items. I can always use more gold in the bank. I haven't yet gotten near the 99-each limit for really rare stuff, but I figure I can address that with Alchemy when the time comes.
Best Answer
This has been unanswered for a while. I think I can offer some guidance.
For a Mage, the best weapon type for your setup is a Wand because you get to recover MP when it strikes, plus you get MP boosts when you put points into its skill.
A Minstrel who heals as a main strategy should probably use Fans. You can get some good ones that heal MP-free when used as an item in battle (such as the Friendly Fan). Remember though that Minstrels are jack-of-all-trades and if you don't switch strategies often then consider a Priest.
Do play with putting these two in the back row. As these two are not using physical attacks you can hit from distance.
Having said that the game logic is said to be broken by some, that the back row makes no difference to attack strength only reducing the chance of being targeted, so it won't matter according to them.