As far as landing goes I have always briefed that in the event of an engine fire below 500 feet we'll sort it out once on the ground. It's much less likely that you'll end up making a fatal mistake that way.
A number of people have talked of landing after LDP on a rig, which is really not a term one should use as it normally refers to Performance Class One Operations and nearly all helicopters that I know of are operated Class 2 offshore. In my company we use the term 'committed' to landing on an offshore deck, this being the point at which a go around is no longer possible and one is committed to landing on the deck. At that point ditching is not an option. If there is much of a sea running it is anyway likely that the helicopter will either overturn or sink, which is a far more dangerous option than facing the wrath of an irate installation manager.
One always has to be careful of fires as I learnt many years ago when operating a Bell 212 offshore in Egypt. I had a full load of 13 in the back, it was around 34 degrees C and just after rotation at about 2 or 3 knots when taking off from the deck of a drill ship (about 60 feet ASL) the No 1 engine started running down (accompanied by that horrid decrease in Nr). Just at that time the No 1 T-handle illuminated, so we obviously had something nasty going on behind
. The T-handle was pulled and engine shut down at which point we had a No 2 engine 'Chip' warning. Speed was now close to 20 knots and I'd decided to fly away when the copilot manually inflated the floats
. The No 1 engine fire warning re-illuminated, but luckily after firing the second bottle it extinguished and stayed out. With the extra drag from the floats we managed a staggering 70 knots resulting in a 1 hour flight back to land. The fire had actually been caused by a failure of the securing nut on the locking plate of the engine oil filler cap allowing the cap to come off and oil to flow back over the outside of the combustion chamber. There was quite a lot of fire damage in terms of paint being burnt off. This had all happened in a matter of seconds and has always brought home to me just how rapidly things can develop if you're ever unlucky enough to have a real engine fire.