The resistor will often be necessary. Raising or adding more in series/ inline, raising it's ohm value will dim them. (Buy a small variety pack of 10-100ohm to dial in needs, then buy more of the value most effective)
Never exceeding max voltage is important to àvoid cooking them, but the current is the driving factor (resistors do a bit of both on a curve set by ohms) , having more current available than needed it just runs full blast. (Not enough, and it won't light.) Voltage can range from min to màx without effecting brightness... i.e. a balancing act; and resistors are often the best thing to balance with.
Solid core, laquer insulated wire, like motor/coil wire, is easy to route and work with.
I fasten it with bends and hot glue dots; just corners mostly. Small diameter, paints, and hides well. (Careful as laquer and hot enamel paint may temporarily desolve the coating of two crossed wires) Two sided tape works too .
It is not overly brittle and can be worked a whole lot before breaking from work hardening.
Heat wire tip with flame or hot solder iron, then wipe burnt paint away well, to get a shine, then tin and trim the wire end if you choose.
Wire size needed will depend on how many led are on a strip, but they don't use much power at all, e.g. way smaller than a diode leg is ok for a few usually. (Like any wire, there is a formula for foot of wire, voltage and amps to decide gauge [or a chart that applies if you know two of the three values])
