Wiring – What gauge wire for irrigation pump

The most important aspect of speaker wire is resistance. There is a ton of junk-science and stupid audiophile marketing claims that will try to confuse you and make you spend absurd amounts of money, but don't be fooled.

Wikipedia actually has a good write-up on it:

Resistance is by far the most important specification of speaker wire. Low-resistance speaker wire allows more of the amplifier's power to energize the loudspeaker's voice coil. The shorter the cable and the greater the conductor's cross-sectional area, the lower its resistance. Depending on the hearing ability of the listener, this resistance begins to have an audible effect when the resistance exceeds 5% of the speaker's impedance.

They also have a chart: for 35' at 8Ω, you're good with 18 or 16AWG.

All you need is basic stranded cable. Don't pay extra for fancy brands, or "oxygen-free" or "hand woven by the dalai lama" or whatever (unless you have the money to burn and really way to, I guess) as there's really no difference -- you can use lamp cord, if you want.

In proper tests, the best audiophiles can't tell the difference between $500/ft "top of the line" speaker wire and coat hangers -- and if you can, James Randi will give you $1 million (sorry, a bit OT from your question, but people that believe in this nonsense really piss me off).

For in-wall applications, you should get wire rated for in-walls - which basically boils down to fumes that the wire gives off in a fire. There's a good article on Understanding In-wall Speaker, Video and Audio Cable Ratings on Audioholics. In short, in a 1-2 family dwelling, any cable with the following ratings is suitable for in-wall: CM, CMP, CMR, CMG, CL2*, CL3*.

If it were me I would probably run 4/0 and mount a 100amp double pole breaker to feed it in your main panel. I'd come out of the breaker with #2 copper and then use a barrel connector to transition to the 4/0 aluminum on each hot line.. Then go the 200 ft in a conduit. In theory you don't need it that thick but I bet you would appreciate the less flickery lights when you turn on heavy loads out there.. You could also do direct burial, they make service cable that is approved for burial and you get a higher rating when buried in dirt because it is basically water cooled. 600v insulation, etc. If you make that trade off you may get annoyed every time you kick on a motor on. They make ul approved barrel connectors for the transition from #2 coper to 4/0 and aluminum and Home Depot carries them. The county inspector approved this method for me. I would call your local inspector and ask him. They are often helpful for the Diy folks when not swamped. Try again in early mornings before they are about, and try more than one..

Jeff