Hi! Some background about me: I've played some D&D 3.5, no Pathfinder yet and my DM experience is composed basically by a handful of sessions of Dragon Age RPG and heavy use of two published adventures, and my group didn't even finished the second one before losing interest on the system. By the way, the players themselves are all used to roleplayng, despite the fact most of them aren't interested in learning much about system rules besides the more basic stuff. Also, the only experience I had creating my own stuff was one improvised session, using the knowledge I had about one village from the videogame to conduct some role-playing for a while because one player couldn't make it.
So the thing is, now that I'm willing to give it a go for an Patfhinder game, which by the way is a much more complex system, I've encountered something that may complicate things a little: my 3 players made an all melle party. One is a fighter, the other a brawler (this guy decided on an assassin background and he won't even own his equipment for a while, only what his handlers will pass on to him to complete specific missions, and he will have to return it after the job), and the only guy who had a deeper understanding of the rules (used to DM) decided on a barbarian. After some pressure from a couple players, I've decided to start my campaign at level 5, better than starting from scratch but at the same time low enough so I have hopes to get my bearings while I go.
We didn't start running yet and I'm a bit lost on how to make adequate harships for them. While I realize I'm a bit too benevolent of a DM, I'm also uncertain how I should exploit the shortcomings of their poor choices, or whether I should do it at all. Any advices?
I suggest you not "exploit" anything. Your job is to make the game fun for them, not to rub their noses in the fact that they made poor life-choices.
The basic problem is that the group will be unable to accomplish a lot of things other than via skill checks. So be prepared to say "yes" a lot when someone asks whether it's possible to use the Athletics skill to impress the King instead of Diplomacy. At fifth level, wizards can fly over chasms, knock doors open, spider climb up the side of a building, see invisible objects (and therefore find them), charm the bouncer into letting you into the party, and still be able to clear a room with a fireball. A fighter can.... hit things with other things.
You might want to use the consolidated skills (and background skills) optional rules to give the characters a broader base of things they can do. And, of course, feel free to make magical potions and whatnot to give them access to the magical abilities they will need to solve puzzles.
There are a lot of types of enemies that will just flat out trash the party. With no healer, they'll be forced to retreat a lot. With no cleric, they'll be at the mercy of any undead they run into. They'll be helpless in the face of invisible foes, and most spellcasting enemies will be able to enchant them more or less at will. You'll either need to use fewer of those than you normally would, or else dumb the opposition down a lot. But this is the sort of calibration that is fairly easy to learn as long as you know beforehand that it will be needed.
It's best not to punish people for playing the characters they want to play. Three PCs is below the norm, which makes it hard to cover all the usual roles (arcane caster, skill monkey, etc).
Giving them a friendly NPC healer might make the game conform better to normal game balance expectations.
Suggestion: The experienced guy playing the Barbarian. Create an NPC Cleric for him to run. Hold on to this character after you have the wands and such and see how that works. Throw the NPC at some point if you feel comfortable and if they would feel comfortable. Unless you think you could handle the extra character. We have had a GM do it but he has run games for years. That's why I suggested waiting.
Wands are cheap. If they're taking weeks to recover per day adventuring, they're being fatally spendthrift. Lots of parties have no healer at all and get by just fine.
If there isn't one rank of UMD among them, well, they might catch the hint by next level. Especially if they find a wand as suggested above.
There's an idea, though: you could try a long-term campaign with lots of downtime between adventures. Not every campaign has to take you from 1 to 20 in a few months, after all.