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*.
You'll end up with two lumps in the carpet that can't be easily removed. You'll also have holes in your carpet at each side for the wire. So unless you're going for the college dorm look, I'd recommend against this. If you do it anyway, the only way to get the wire through this is to attach it to the existing wire and use that to pull it through. I doubt the magnet idea would ever work, and trying to push the wire through would just fold on itself since it's not rigid enough.
As for the way I would do it, the easy way is to pick up a box of nail clips and tack the wire down around the baseboard. With these, you can pull the nail slightly and spin the clip 180 degrees to easily add or remove a wire behind it. After enough time and especially enough furniture, you tend to forget they are even there. You can also have a nicer look with some wall mounted conduit.
The excessive option is to open up the floor or below ceiling and run flexible conduit through the floor, preferably with the ends in the wall behind a modular plate with the appropriate connectors installed. If you happen to already have a wall and/or ceiling exposed, running conduit would be a great idea, I only consider it excessive if you're pulling down an existing wall to install it.
Best Answer
Well, the way I'd find it would be to get a wire tracer. These consist of a transmitter that hooks to one end of the wire to use it as an antenna, and a short-range (and sometimes directional) receiver which you can then use to find the wire emitting that signal. That will let you trace a wire through the wall's surface. (There are several variants of this, at different price points; the more expensive ones can even be used on live AC circuits.)
[Originally a comment, since I thought it was a bit short/shallow as an answer.]