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: 
I play RoleMaster but the idea of XP is similar. 

The answer is in the word. I give experience points for relevant **experiences**. I dole them out (in order) by:

1. **Milestones**: Accomplishing a mission or reaching a certain plateau
2. **New experiences**: first time ever in town, picking a lock, meeting an owlbear, etc. (2nd time in a town, not such a big deal),
3. **roleplaying**: more on that later,
4. **Hits taken or received** (relative to monster difficulty),
5. **Spells** successfully thrown (relative to caster's level),
6. **criticals** (RoleMaster is a critical heavy playing system),
7. **ideas/specials** ("It was my idea to trap the gelatinous cube in the giant
squirt gun."),
8. **kills**, and
9. **treasures** (treasures are their own reward, in my opinion, and players usually don't get any XP for gold and magic items).

Rearrange or add to the list based on what is important in your campaign.

I also, with each new level, give the players a blank "Experience Sheet" form which has areas for hits taken, given, spells, ideas, thing encountered, etc. It's their job to keep track of things they've done individually on these sheets and I collect them when I'm going to award XP. (It's funny what some of them will put down to wrangle extra XP sometimes!) When I really like the way a character is playing their character (i.e. a character sniveling in front of a noble, polishing his boots, acting as a decoy) I make sure that the player wrote it on their sheet or I write it on a master sheet I keep for just those occasions.

Because I place the group activities highest (just watching an Owlbear rip apart your fighter is an experience), the individual experience is fairly well grouped with the more immersed individuals ending up getting a little bit more.

Hope this helped.
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).