[Jhiggy]

Here is some of the least inexpensive rope I have found. Cajun Ropes » Cajun XLE They have different types but the XLE is the "high" quality stuff. For your sheets I would do either 1/4 or 5/16. On my Lido 14 I opted for 5/16 because it is easier on the hands and 1/4 felt a little too small to me. For all other lines I went with 1/4". I have received the lines and am Very happy with them. When I ordered them it took a couple weeks for him to respond so don't get frustrated if it takes some time.

Edit: You could also get away with the Dinghy braid but they only offer it in 1/4 as the biggest size.

 

[Jhiggy]

Braided is best for running rigging. It's the lowest stretch, won't kink as much, and is much stronger for the same size. That being said if you opted for 3 strand it would probably work just fine. That boat probably originally had 3 strand on it. Is there a reason you will need to splice it? Braided is much more difficult to splice but if you had to you could always do a whip splice.

 

[Jhiggy]

If you go braided a halyard knot would work. Jeanneau Halyard Knot

Just giving you options.

 

[Jhiggy]

Yep on both my Halyards that is how I attached the line. On a small boat like ours there isn't a huge amount of tension on the halyard. Although in the pictures it looks like they are using it to attach the line to a big boat.

In terms of which line I would go with. It depends on how much money you want to spend. If money isn't a big concern I would instantly go with New England Ropes. It's probably one of the highest rated rope. For my climbing ropes I have purchased in the past I only trust New England. Just like anything you'll probably get people recommending all sorts of rope.

Because I'm a cheapskate I went with Cajun Ropes. After pricing them out it cost about 40% less than New England. I haven't had any problems with them yet but I'm on my first season. Someone else in the forums recommended them to me.

Edit: Oh! And if you want to try splicing the braided rope here is a great PDF created by NE Ropes. http://www.neropes.com/Resources/84906_NEROPE.pdf If you were going to try your hand at splicing I would probably order the line a little longer than needed in case you need to try the splice a couple times. In the guide it tells you how much line is required for the splice so you can judge how much extra to get.