Normal sugar can give a cidery ' homebrew ' taste to the beer and is normally responsible for raging hangovers.
Glucose / dextrose is a more refined sugar, which helps the yeast do its job better and gives a cleaner ethanol (alcohol) while fermenting.
Spray malt / DME / spray dried malt extract is a malted grain sugar, exactly whats in your beer kit (except your beer kit has hops too)
Using DME gives a fuller bodied beer, but doesn't fully ferment out all the sugars, so generally needs to be offset with more hops, unless your aiming for a malty finish to the ale.
BKE is a mixture of maltose and sucrose.
I would be dead against the Tate n Lyle houshold raw cane sugar in all instances, unless you start inverting it and seperating glucose and fructose molecules.
Brewing sugar (glucose powder) gives a cleaner finish, but its still not the best.
BKE - beer kit enhancer is a good step in to raising the ABV of the kit but also retaining body without it finishing too sweet.
DME if you want a full bodied beer.
Confused?
I started a Breferm Diabolo kit today, 9 litres of Belgian 8%abv largerish ale
For that I cooked up a bag of sugar, cup of water and a tsp of citric acid to make inverted sugars - aka candi sugar to try and keep it authentic to the bottled /casked version.
Got a brewferm Grand Cru to put on next week, but i'm currently trying to reculture the yeast from a bottle of Brakspears Tripple - bottle conditioned to use for that project (and to keep the yeast culture going for some extract / biab brews)