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.
It as been awhile since I have been able to DM, however, I have always believed in a very simple system. Most of what I was taught growing up with the game is posted here, just in different variants. 

I have always taken the campaign as a whole. The completion of the campaign creates x amount of experience. 

Roleplaying is required by all members. Those who actually role-play their characters get experience points for doing so. Those who are along for the ride will find the struggle to level up harder.

Character Class tasks: A fighter is expected to fight, wizard expected to fight with magic (offense and defense) or use their spells to detect the out of the ordinary things In the world. Clerics are expected to fight, heal and protect from the supernatural. Rogues are expected to fight when it is advantageous to them (sneak attacks, back stabbing, etc...), detect traps, remove traps, pick locks, etc...

These tasks are rewarded on a simple method. If they are a bystander and watch, they get experience points for the experience (small amount) but those who actually are involved in the character class task get rewarded for success or failure with more xp for success. 

Attacking and killing creatures is part of the total campaign xp. I truly believe in the keep it simple stupid method. (KISS).