First of all, Welcome to our site and to the hobby of casting!
The answers to all of your questions are, it depends!
Smelting ;
What kind of pot and burner do you have or plan to get? If you are doing 10-15 pounds at a time with an iron skillet on a camp stove it will take you several hours. If you have a Turkey frier burner and a cutoff propane tank for a pot you will probably be 4 hours on 2 5 gallon buckets of weights. It depends on whether you have to store your smelting gear away or leave it set up.
Casting;
What type of casting pot and molds are you thinking about. With a 20# bottom pour pot and a 4 or 6 cavity mold you could get several hundred bullets in 2 hours. Once again, set up time will cost you. Can you leave your casting pot set up or will you have to store it away?
Sorting weights;
There are a few stickies about sorting weights. Some casters don't sort and try to keep the heat under the melting temp of Zinc. Thinking the Zinc will float to the top to be skimmed off. Others sort and only have lead weights in the pot. Once again, the question comes up can you sort for an hour or so and leave everything out or do you have to put it away?
My methods;
My smelting pot will hold 400 pounds of molten lead and my burner will melt it in 20 minutes or so. I use 8 of the Lyman style ingot molds so I don't have to wait on them to cool off between pours. I use a nice Rowell Ladle and a heavy duty skimmer. I have maybe $100 invested in the two of them. The time they save was worth it to me. I save wax products and sawdust for flux. I usually save my scrap all year and a buddy and I will spend a day melting his and mine. It helps to have some help. To do your 2 buckets of weights would probably take me 3-4 hours to melt, counting time for set up and putting things away. Once set up I can have 400 pounds of ingots about every 2 hours. I have to put my smelting stuff away, but its in the corner of the shop near where I use it.
I cast with an RCBS ProMelt pot that holds 20 pounds of lead and I cast with 4 cavity molds. It probably takes me 45 minutes to get my first bullet. Loading the pot, cleaning the mold, pre heating the mold, lubing the mold, staring and fluxing the pot --- yeah, probably 45 minutes to an hour to get started. I figure 300-400 bullets an hour after getting started. I can leave my pot and everything on my workbench if I want to avoid the set up time.
Sorting weights. I hand sort, picking up each weight and looking at it. I use a pair of electricians dykes to make a test cut on any suspicious weights. I sort until I get tired and quit. I try to sort as I acquire weights so as to not be hopelessly behind. I've never checked the time when I'm sorting. I can leave the buckets where I sort, not having to put them away or get them out.
You are right to expect some wasted time and lost production the first few times you do each of these processes. But you will develop a technique and a comfortable way to work.
I hope you can find something useful out of all of that!