The spellings with 's' are British whereas the Americans use 'z' where the sound is of 'z' for instance the examples you mentioned explain it very clearly (modernisation, centralization etc).

The thing to keep in mind is to remain consistent with whatever mode of spelling you decide to use. In the essay paper this year, the last topic was about labour saving devices but if you look at the question paper, you'll find that it was spelled as 'labor' which is the American way of spelling it.

Just be consistent. You want to leave a good impression on the examiner, consistency is the key to that. Just make sure you don't mix these common things. I'm ordering these in British first and Americans second as I personally use British spelling for my writing.

'ou' vs 'o'
Major examples include colour/color and humour/humor. Here, the the (first) ones with 'ou' are the standard British way of spelling things.

're' vs 'er'
centre/center and theatre/theater are good examples of this. Once again, the first ones are British and the second ones are American. I'll be sticking to this convention in the remainder of this post.

'ise' vs 'ize'
realise/realize and organise/organize are commonly switched words in this category.

'yse' vs 'yze'
analyse/analyze or paralyse/paralyze are examples of these even though these words are less frequently used.

The extra 'l'
For example in traveller/traveler

Missing vowels
Oestrogen/estrogen or paedophile/pedophile are examples of these.

'ence' vs 'ense'
offence/offense, licence/license or defence/defense are examples of these. Simply put 'ence' is British and 'ense' in American, no weird rules apply. Easy.

'ogue' debate
dialogue/dialog and analogue/analog are examples of these.

You may find many more examples of these, and others that I may have missed because of my limited knowledge, but these are general rules that'll help you whenever you find it difficult to decide which spellings to use. I hope it helps.

As far as MS Word is concerned, go to the settings and choose British English for the dictionary, you'll be set to go and they'll be no more nagging in the future. Best of luck.