Hi gitaardocphil and KMajors!
I'll respond to KMajors first, since it seems a relatively easy question to answer, and this is really just my opinion (I own 14 -16 guitars, at least that's how many I can see in this room). Decent-sounding and durable electrics for under $300 are rare. I'd look for example at www.guitarfetish.com and their Xaviere brand, or www.rondomusic.net with their Agile or SX brand. These guitars are made in Asia, but the importing companies usually control the quality before they ship out a lemon.
Personally, I also like some of Musiciansfriend's Rogue brand. With all thre companies, you'd be better off buying something around $200 -or more if you can afford it. My rule of thumb is: anything under $150 retail is not worth bothering with. Both Gibson and Fender have low-price lines (Epiphone and Squier). I own one of each, because they were cheap, but I cannot recommend them. A little higher in price are Fender "Standard" instruments, usually made in Mexico. For $400 you get a very decent sounding, quality electric guitar. Take your pick: Standard Stratocaster, or Telecasters made in Mexico are pretty decent and will last. Epiphones that cost from $399 are also ok -not great.
When you buy an electric, prepare yourself for the cost of an amp, tuner, cables, gig bag, etc. that you will want later...
Gitaardocphil: Even among "famous" tone-woods, there are distinct differences in quality: Take spruce for example. The quality is measured by the density of the wood and to a certain degree by its "figure". Slower growth of a tree results in tight grain. There is even a Standard: AAAA is the best, with AAA and AA to follow. Some suppliers also invent their own grading, such as "Master Grade". The difference in quality also shows in the price of the raw materials. Many commercial guitar companies resort to laminating a thin good looking vernier (German: Furnier) onto a layer of less expensive wood. In general, solid tops and even solid backs/sides are preferrable. I am not exactly a master luthier, but more of a "guitar builder". It's easy to ruin some nice expensive wood with just a moment of distraction, or bad planning. That's why I'm slow... I just want to learn how it's done, so I can then actually play the instrument and be proud of it.
Necks for acoustics and electrics can be made of Mahagony. It's easy to shape (and to ruin), good looking, and a nice tone wood. Fender uses maple for electric necks, because maple is much stronger than most other woods. It's not as easy to shape by hand, but of course Fender uses machines for those tasks that a luthier would use handtools for. There seems to be a difference in tone, using maple, ebony, or rosewood for the fretboard: rosewood is neutral sounding, maple can be harsh, ebony is best (again my own opinion).
Do I measure tone? I use an oscilloscope to observe waveforms generated by electrical pickups. These vibrations are initially influenced by the tone woods. You can observe "sustain" and "attack" and "volume", and also harmonic content and overtones of the instrument, but I cannot safely say that I know exactly what I'm seeing -probably would need much more experience with many different guitars. The pickups, or microphonic devices also shape the sound -not an exact science for me at this point.
What I can hear is this: If an instrument sounds pleasing without an amplifier, it usually sounds great when amplified. Bracing does influence the tonal characteristics. I've experienced that myself a few months ago. I played a black Martin Johnny Cash Commemorative Acoustic, and after just the first chord, I was hooked! This guitar retails for $3500 -good for me, because I can't buy one that expensive. When I played the first chord, the sound coming from the sound hole all of a sudden filled the air around me. I felt the guitar reaching out to me, saying "Buy Me Now, You M@#$%^&cker!" I was so shocked that I hung it right back on the wall -creepy!
What was this guitar's secret? Innovative "Forward Bracing". A technique invented by Taylor: the center brace is moved forward by an inch, creating different angles for the side braces. The guitar resonates now a lot better (louder) and sounds full and rich. It's funny how Taylor had copied the Martin bracing scheme for years, then invented something new, and now even Martin is using this relatively simple modification to make their instruments sound better...
Just started a flickr photo page, check it out: http://www.flickr.com/photos/23752184@N04/
Play on!