Not sure if your still looking but I'm a fan of Samson ropes, I have nothing against other brands it's just my preference. For light rigging you do not need anything larger than a half inch rope, Samson stable braid 1/2" has a breaking strength of over 10,000lbs.
Stable braid is great for using as a pull rope and a rigging rope with rigging rings or blocks, not natural crotch. It has little stretch. This rope is an industry standard as it knots well, is easily spliced, and has superior strength.
Samson Hawkeye is a 16 strand rope it is one of their 16 strands, all 3 of them are the same construction with the only difference between ropes being the color. This rope is designed as a climbing rope but makes a great light lowering rope, MBS (minimum breaking strength) of about 8,000 lbs if I remember correctly. It works well in rings, blocks, and natural crotch. It has some stretch
Samson true blue is a 12 strand rope, has many of the same characteristics as the 16 strand, also designed as a climbing rope and excels at all 3 rigging styles. This rope holds up to natural crotch even better than the 16 strand and has more stretch.
3 strand rope can be used for natural crotch but does not work well with hardware. If you look at the construction the more parell that the strands are with the rope direction the better that it works with natural crotch, 24 strand (stable braid) is almost perpendicular to the rope's direction and will glaze or melt when used natural crotch.
Stretch in a rigging rope is not necessarily a bad thing, it is just something to consider in each situation. The stretch in a rope can help dampen the shock load when rigging pieces out and can also help add a little extra pull when using as a pull rope. As a negative when rigging in a tight situation such as close to a roof, the stretch in the rope could cause the limb to make contact with the roof.
I buy most of my ropes through treestuff but they are located 3 hrs from me so shipping is fast. If you do not need a long rope wespur sells random lengths at a discounted price as a clearance rope.
As for the throwline I often never need more than one throw weight. If you girth hitch the line onto the ring with no other knots in the line, just leave about a 3" tail, then if the throw weight were to hang up just pull hard and the throw line will come off of the weight. Most times it is a combination of the throwline and the throw weight that cause them to hang up and once they untie themselves both will come out of the tree. Another tip is when you throw it do not stop the weight until it's on the ground unless its headed for a valuable. The sudden stop of you grabbing the throwline will cause the weight to wrap around twigs and limbs, not to mention the possibility of the line cutting your hand. Last tip for now is if you do not get the throw that you wanted but the weight makes it to the ground, untie it before pulling it out. This will allow the string to come out without hanging up and prevent a throw weight from coming down onto your head as it free falls out of the tree.
