You can use this chart to determine your gauges, and keep in mind it’s usually better to use multiple sets of smaller wires in parallel, to reduce heat during soldering and build in some redundancy.
The standard insulating materials here are fish paper and kapton tape.
If you’re referring to wire that acts as a fuse for each cell, that’s typically not done here in the world of esk8, since one disabled cell will screw over the whole pack anyway.
Most people here use either a kweld or a malectrics spot welder, which you may be able to rent or lend from someone on the forum. Spot welding batteries is pretty difficult to get consistent results with, you should expect to have to do a lot of practice before building your first pack.
Just be aware that you’re biting off a big project, and you should ask for feedback from forum members as you go to make sure you’re not making an unsafe battery. I second the recommendation to read the battery builders thread for a while before starting.