Helicopters departing a land base for an offshore installation must carry enough fuel to make an approach at the offshore destination and (if a landing is not possible) then have sufficient fuel for an onshore diversion where the weather at the ETA must be above certain limits.
A coastal airfield is one which is invariably near the coast and so long as it is approved as such then it is possible to nominate it as a destination airfield without an alternate if the weather limits are >600 foot cloud base and >4km vis by day at the ETA. This is obviously preferable as alternate fuel does not have to be carried allowing a greater payload for the customer.
ARA limits as TTT said are 0.75nm and if the rig is not visible then a missed approach must be carried out. If there is sufficient fuel then another can be attempted. Minimum descent is usually a radalt height of 200 feet during the day and 300 feet at night but each company sets their own.
Other limits to be considered in rough weather are the pitch, roll and heave limits of the rig deck for each helicopter type. These are relayed to the crew before the approach can begin. If they are out of limits then it is a waste of time making the approach as a landing is prohibited.