Neck woods do more to influence the guitar's tone than you'd think. In fact, it's number 2, right after the pickups. Which makes sense, its the wood that runs under most of the strings themselves. Body wood does a little less than the neck, especially if you're a Thinline junkie, like me.
Maple is bright, regardless of fingerboard. So coupled with Single coils (typically bright) and an ash body (also bright), and you've got a bright guitar. Poke around on the Warmoth site, there's a wood description page that gives a breakdown of what woods give what tone. Something funky is up with the site, I can't seem to pull up warmoth.com, or I'd link it.
But.. for necks:
Mahogany and Rosewood are dark, Maple and Padouk are bright, and Goncalo Alves and Wenge are in the middle.
For Bodies:
Mahogany is Dark. Ash is bright. Korina is in the middle, but closer to Mahogany. And Alder is in the middle.
As far as your amp is concerned, you're essentially plugging it into a PA. You're hearing the sound of the guitar, raw and naked, and not run through a traditional guitar amp. This will also make a huge difference. Its okay for some applications, but IMHO you end up with some uninspiring tones. I recommend... yes... spending money... pickup up a small modeling pedal, like a Digitech RP55 (
http://guitars.musiciansfriend.com/product/DigiTech-RP55-Guitar-MultiEffects-Pedal?sku=580861). Its on the very-cheap end of the amp modeling spectrum, but when I've used modeling units (and I do a lot) the secret is to exercise self control, don't turn anything all the way up, keep the gain down, don't use effects (seriously) unless its just a wee bit of reverb. In fact, when it comes to tone, your amp has way more to do with your tone than the guitar. There's no shame in using modelers either, unless you're a Stevie Ray Vaughnabee, in which case.... oh damn.. I almost went into a rant.... anyway, the electric guitar needs a guitar amp, or modeler, in order to get you to the tone you want, unless you play jazz.
You're gonna need something amp-like, eventually. Otherwise you'll look like a dork, I have a friend who saved up $1200 to buy an amazing Godin LGXT, and then couldnt use it because he had no amp, acoustic gutiar amp, MIDI unit, or anything to plug the MIDI unit he didn't have, into. He needed, at minimum, to spend another $500 to play it!
You might find a drastic difference if you take the Lyon and plug it into an actual guitar amp or modeler. And don't be afraid to dial the knobs around or use the guitar's tone knob, or even roll the volume knob back a hair.