This could become a book if we give you all the details, but instead let's address what most cruisers use and some general hints on what to look for. First of all there are a few different types of lines you can choose and the most common ones are:
Riggers Braid – Low stretch core with a softer, looser outer cover which allows for splicing and is preferred for sheets as it coils and handles comfortably.
Southern Braid / (Yacht Braid) – Same low stretch core as Riggers braid however an outer cover made with a higher total amount of stains thus more durable and commonly used for Halyards and lines which run over blocks and sheaves.
Dyneema Spectra Braid – These are the ultimate in control lines with virtually no stretch at all, they are lighter and have a much higher working load allowing you to go to smaller size lines, however make sure they will fit your winches and or blocks. If you are looking for better sail trim that remains these are the ultimate lines to have as sheets, or at least as any halyard on your vessel.
Once you know which lines are best for your boat it's time to buy, it is important to check what size you need. They generally range from 8 to 18mm and jump up in size by 2mm at the time. As to length you might be able to find this in your boats details or as a general rule you could follow these guide lines:
Halyards: twice the mast height plus 10% if sail is hoisted at mast, or 20% if sail is hoisted from the cockpit.
Jib Sheets: 1.5 times the overall length of the vessel.
Spinnaker Sheets: 2 times the overall length of the vessel.
If your present line is sufficient in length take it to the store as they can measure it and provide you the correct replacement.
Maintenance is relatively easy. If you are not using the lines, such as jib sheets, take them forward and hang them on the sail or bowsprit as this will prevent them from taking on dirt and reduce chafe from the deck. If and when the lines get dirty and start to become stiff but they are still good, soak them in warm or hot water with washing soda for about a day or two than rinse a few times and hang to dry - they'll be like new.
Splicing lines should only be done with new lines.
If you are sailing to distant places it is always good practice to carry at least one spare halyard plus some extra line that can be used for the main sheet, boom vang or similar application.
Gypsy Blues – Our boat is fitted with Southern Braid for halyards and Riggers Braid for all the sheets. As we travel distant places we always carry 2 spare halyards and have spare jib sheets plus some general lines which can be used in different areas.