The Battery isn't going to be the determining factor for what type of wire to use. If you have a Mech mod, I highly recommend you don't use it until you have a full understanding of what is involved with Mechanical mods. They can be dangerous if misused.
I recommend that you get a regulated mod to use. Much more forgiving of mistakes as regulated mods provide quite a bit of protection for batteries.
Wire types for the most part are:
Stainless Steel - SS - Can be used in Temperature mode or Power/Wattage mode on a regulated mod. Ramp up is fast compared to Nichrome or Kanthal. Resistance is low so better for subohm coils rather than high ohm ones. Slightly springy wire.
Titanium - Ti - Can be used in Temperature Mode only on regulated mod
Nichrome - Can be used in Power/Wattage mode only
Nickel - Ni200 - Can only be used in Temperature control mode on regulated mod
Kanthal - Can only be used in Power/Wattage mode.
The gauge thickness of the wire is going to make a lot of difference in the end coil ohm you end up with. Here is a calculator that will give you an idea.
Coil wrapping | Steam Engine | free vaping calculators
There are lots of options for mods and tanks. So hard to say what would be to your liking.
Those batteries are suitable for most mods. You need an external battery charger as it is not a good idea to charge in the mod generally
Here is a decent mod and tank that uses only drop in factory coils. The tank is more of a direct lung vape tank. This can be found for around $70
Aegis Legend Kit
There are lots of others but you need to know what you are looking for before coming to a decision on what to purchase.
This is good older tank that comes with an RBA that would allow you to build coils and gain experience. Pretty easy to use. The Tank also takes premade drop in coils with many different coils available. Tank will work with most any 510 pin mod.
$22.41 Authentic KangerTech Toptank Mini Sub Ohm Tank Clearomizer - 4ml / 0.5ohm / stainless steel + glass at FastTech - Worldwide Free Shipping