Question: So I'm creating my first D&D 5e campaign and I want there to be an even balance between combat and non-combat with a slight bias to the non-combat style of missions. However I'm unsure about how to deal out XP for these situations and how much is a suitable amount. Also should I some characters get more XP than others for certain missions? For instance if you're trying to steal an artifact from a temple then a rogue will be very good at this while a barbarian will likely not be able to do much and so deserves less XP than the rogue but is this a fair way of managing things?

Answer: 
You can also award XP based on how important the non combat event was toward progressing the general adventure. A technique I have found to work fairly well is to take the party's average level as a base CR. Tiny inconsequential events (ex: talking to a shopkeeper in character) are worth CR minus 2 as an experience award. Moderate events (ex: finding an important clue, or procuring a map of the area to be adventured in) are worth CR minus 1, while events upon which the adventure hangs (ex: Tracking down the BBEG's lair, unmasking the Evil Prime Minister) are worth a full CR. Award experience per the CR values given in the Monster Manual and DMG.

Thus if the party has an average level of 4, then finding an important clue has a CR of (4-1) or CR 3, and is worth 700 xp. If the characters were 3rd level, it would be worth 450 xp.

The nice thing about this is that tying the CR for the event to the party's level will tend to scale it with the characters, so that they never lose the incentive to find non-combat solutions, or to forgo non-violent interactions with the environment. Note that my values work for my campaign. Adjust and season for taste.

One last thing, if you do adopt an approach that rewards non-combat interaction, make sure the players are aware that you are doing so. If you don't tell them, they have no incentive to try alternative behaviors.
I will answer this on a generic level, as I have not gm'd a dnd game yet, so keep that in mind and fill in appropriate game system constructs for yourself.

In general, I dont feel like its a good idea to hand out experience points on a per enemy or interaction level. In other systems, particularly TDE, I will hand out the same experience points for everyone at either the end of an adventure or at critical points where it makes sense. 
Every player will get the exact same amount of experience as everybody else. Why? I have found that if I hand out experience individually, I risk to get several problems:

1. Kill-Stealing/Opportunity Stealing
2. Split of Power
3. Adventure Design

Now what do I mean by this?
The first point may be detrimental to cooperation. Your players may start trying to rush into situations without prior thinking, just to get extra experience, or similarly, trying to outplay each other in timing the moment to get more experience faster. Now this is probably not what will happen to you if your players like working together or if your encounter design is difficult. It may, depending on the "Social encounter" design, still occur though.

More pressing is a split of power. If a player happens to consistently have more opportunities than other players playing into the pcs strengths, a player may rush ahead in level of power, making balancing the encounters harder.

The most important factor I feel is mission desin and its impact on the "fun" of your players. I believe the GMs job is to make the games equally fun for everyone present. This also plays massively into the way you design your adventures. If you design them in a way that does not allow everyone to play important roles, the respective players will probably be dissatisfied afterwards. If it happens once, no problem, but more often...
So, If you want to do this, make sure you have have at least some opportunities for everyone to shine, at the very least you'd have more opportunities in the next adventure for those players disadvantaged in the current one.

In the end, its up to you, BUT I would advise on giving the whole group equal experience points and encourage the development of ideas and tactics more than actual mechanical performance. The only exception I would make is for good roleplay. Good ideas should result in an *overall* increase of experience to be handed out, not specific for individual players.

TL;DR:

If you have a competitive group or want to encourage it, while at the same time you're willing to spend extra effort on balancing each adventure in itself and towards the previous/next ones, go ahead and hand out individual experience points. 
As a modification for this, try not only to hand out XP for the actual interaction, but also for Ideas.

However, I'd pool up experience and hand out the same amount for everyone, except for special occasions where you feel good roleplay needs to be rewarded, similar to what @Jason K wrote.