Upgrade cranks, chain, gears on a Carrera Vengeance MTB
ANSWER This is a bad idea.

Your bike has 24 gears total, so its probably a 3x8.  Thats three front chainrings and 8 cogs on the rear.

You could get more road speed by having a smaller small on the back, or a larger large on the front.  However the default rear cassette is 11-32 and 11 is as small as they go.  Your specs don't say what the front chainrings are, but on a triple MTB they're likely 26/36/46 tooth, or similar.   If you put a 50 tooth front chainring on, then the FD has to be able to get there.  Most simply can't handle more teeth.

If I were you I'd look at the gear cables and see that they're moving okay through the outers.  The inner wires should be shiny and slide easily.  A new set of inner/outers will cost you a lot less than a group and should help sort your shifting.  Also measure your chain for wear (ie stretch) and if its over 1% elongated, replace it and the rear cassette if it is worn or starts skipping.  

You ride on the road a lot, perhaps you could consider a dedicated road bike?  If you've got the budget to buy a new groupset, you're within spitting distance of a complete road bike anyway.  And then your N is 2.

Summary: You're on a hiding to nothing doing expensive part upgrades on almost any bike.