You're in conduit, use individual wires - they are cheaper, they pull easier, and the conduit fill on cables is terrible.
Typically we shoot for less than 3% voltage drop at rated current. Less drop is OK.
I'm fairly sure you need 6Ga wire minimum for a 60 Amp feed - given a short 30 foot run, this is also probably perfectly adequate. I'm getting 1.8% drop for 60 amperes at 240V on 30 feet (one way) of 6 Ga. Edit - Copper!
The limiting temperature rating if using THW, THHN, etc wire is generally the temperature rating of the connectors on the service equipment (breaker or panel) which is usually 75 C - even if using 90C wire, you have to follow the 75C section of the table due to the connections.
Copper .vs. Aluminum.
Copper (Cu) costs more, Aluminum (Al) less.
Copper has better conductivity - effect being, smaller wire to carry the same current. In this case, 6 gauge copper .vs. 4 gauge aluminum.
Copper oxides are conductive. Aluminum oxide is an insulator, forms quickly, and sticks very tightly to the wire. Aluminum connections need special procedures and materials to make a solid connection that won't get loose over time and overheat. These include things like brushing the wires with a stainless steel brush and an aluminum wire connection compound that coats the wire to prevent contact with air. The connections themselves must be rated specifically for use with aluminum, but most large ones will be (generally marked Cu-Al meaning they work with both, where unmarked connectors are assumed to be copper wire only.)
Aluminum connections are further complicated by cold flow, but that gets long and complicated to get into, and is supposed to be addressed by using the proper connector types. Essentially the connection gets hot, the wire swells, the swollen wire deforms, the wire shrinks, the connection gets looser, so next time it gets hotter, repeat until fire.
Wrong kind of staples. Eventually they might all abrade the cable, whether or not you stapled right through it and present a fire hazard. Replacing the cable would be best. Inspecting the damage would be good, but then you'd have a splice to deal with or have to re-insulate, both having to be waterproof. Damaged insulation can be fixed, but we don't know how bad the wire got nicked (also a fire hazard).
Plastic Insulated Cable Staples: (Ideal)
Best Answer
That cable is old cloth jacketed nonmetallic cable. I would say by the 1970's, this was no longer being installed, nonmetallic cable in the 1970's had a plastic jacket not too much different than what's used today.
The ground wire was considerably smaller on the old cloth jacketed cable, and the early plastic jacketed cable. I see a lot of old 12-2 romex, which was white back then rather than yellow typical of 12-2 now, with a 16 gauge ground wire. The smaller gauge of the ground wire isn't usually an issue because it's usually not normally carrying current, it's intended to just carry fault current briefly so the breaker trips (or back then, the fuse blew). In some situations, the fault may not clear, and it's conceivable in those situations the wire could become overloaded, but that's unusual enough I don't think it's considered a major concern.
If the insulation is undisturbed, it's usually fine, but if it has deteriorated with age, it can be brittle and crumbly, so it's best left alone. It's especially prone to deterioration if it's been subjected to a lot of heat - in attics, above light fixtures, etc.