15lb main line should be plenty in respect of strength, and the thinner the line, the better the feel. However, my friends all run 20-30lb main line with new age (8-strand) super thin braids, so I'm in the minority with my 14lb original 4-ply Fireline.
I run 10-20lb mono leaders that start the day with the knot just outside of the baitcaster's eye. As the day progresses and I cut off or break off, eventually I'll be down to 4'-5' and will then re-tie.
Last fall my fishing buds and I filled our glasses with grape sqeezing's and used hand scales to test join knots. The best, quickest knot I've found is a 4-wrap Surgeon's Knot (also illustrated in Geoff Wilson’s books).
1. Take the single strand of braid and the leader and overlap them about 9"
2. Wrap the leader around the braid 20 times (or vice-versa: just twist them together). [Make certain you have enough of a tag on the (slippery) braid that you can get a grip on it later when you’re snugging up the knot.]
3. Make an overhand knot with a loop at least as a big as a US quarter (2cm) and pass the tag end of the leader through it 3 more times (i.e., a 4-turn Surgeon's knot). (This is easier to do with shorter leaders but it’s no BFD to pass 5-7 feet of mono through the loop each time.)
4. Pull on all four ends slowly. The mono will tend to cinch faster than the braid. So pull on just the braid to get the loose loops out. Pull this knot up dry.
5. Tighten down into a small knot with no loose loops. (If there are any, cut and re-tie: only takes a minute.)
This knot is very small and winds on any reel. The knot typically breaks at 75%-90% of the actual strength of the mono.
A knot that can pull out with thin braid and/or a leader lighter than 25lb mono is the improved Albright (or "Alberto's Knot"). It's tied in a style that's the reverse of the more fashionable FN knot, which is to say that the mono is bent in a U-shape and the doubled braid is wrapped away from the "nose" and then back down. In more detail:
1. Make a loop in the mono/ fluorocarbon, pinching the two lines about 3" from the end
2. Insert the end of the doubled braid up through the "nose" (end of the loop) and leave about 5" sticking through.
3. Wrap the double around the loop 5-6x going AWAY from the nose.
4. Stop and wrap the double another 5-6x times BACK TOWARDS the nose
5. Pass the end of the double out through the nose the same way it came it.
6. Grab all four ends and snug up. Once the knot starts to seat, drop the two tags and PULL like crazy. Properly seated, the wraps of the braid will look like a whip-finish.
Caution: There should be a 1/4" fold of the leader material (the end of the "nose", so to speak) peeking out of the wraps. This is to keep the knot from slipping off the end.
7. Trim all loose ends tight and you're good to go.
The knot reels onto most standard baitcasters, so you can use long leaders. However, I start the day with the Improved Albright just outside the reel. It casts without a problem. Breaking strength is usually 85% of the leader material.
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Couple of other pointers:
1. Please tie and test break your own knots ahead of time. Your style has a lot to do with how they break.
2. Don't be fooled by knot breaking strengths by using published line strengths. I typically knot 15lb Chameleon (breaks at 17-18lbs when fresh) to 14lb Fireline (breaks at 22lbs) and achieve 15lb breaking strength (85% of actual mono) with the 4x twisted Surgeon's knot. If you use 20lb Fireline, it breaks at 33lbs. I read about people using inferior knots that break at 20lbs (say) for their 20lb braid and declare them "100% knots." Uh, no, you have a 67% knot.
3. Uniknots are typically very weak and/or pull out. Even doubling the braid before tying the uniknot doesn't help that much. Don't believe me? Get a set of scales.