After playing acoustic for two years I switched to electric about 3 months ago when I bought my first electric guitar (but not last), a 1997 Epiphone Les Paul Standard. I put a set of Super Slinky strings on it and tuned it up. Now the amp I have is an old Crate travel amp that used to belong to my dad back when he played rock. It's seen better days so to speak, and I want to replace it with another amp that I can travel with but won't break the bank. The music I'm currently playing ranges from bands like Muse, Judas Priest, Led Zepplin, Foo Fighters, AC/DC, Lynyrd Skynyrd and so on. Any recommendations?

Another question that may be hard to answer. Dad also has an old Aria electric guitar with strings that are long past dead. I hooked it up to the amp and played the A power chord on the neck pickup. I then did the same with my Les Paul. I noticed the Les Paul seemed "muddier" when the A was played on it, while the Aria sounded crisper and more like an A power chord. Any idea why this is and what I can tweak to make that power chord become more "crisp" on the Les Paul and less like a jumbled up sound?

These things are so subjective. Honestly your best bet will be to go to a music shop and try out a bunch of different brands/models. See what you like regardless of price. Once you know more or less what you like tonally, you can start looking for a specific model that fits your budget. Based on the bands you list the obvious first-choice would be a Marshall. Especially with a Les Paul you can really get that classic crunch sound pretty effortlessly. Start narrowing from there. Like something crisper? Try Fender. Want more solid-state action? Maybe you'll like Orange. So on. Then you'll find every manufacturer has models in different price ranges depending on features, power output, combo vs stacks, and on and on. So if you decide you like Marshalls, for example. you can find combos for $600 or so, or keep your eyes out for used deals.

Personally if I were buying an amp for myself right this moment it wouldn't even be a question, I'd fork out for a Boogie Mark V and it would break the bank. But that's because I've been playing long enough to know exactly what I need/like. I've been playing an older Mesa for over a decade and paid $1000 for it at the time, but it's been one of the best purchases I've ever made in my life. But it's all down to taste and playing style.

As for the tone of the Les Paul that sounds right. Don't use the neck pickup like that, that's what the bridge pick-up is for Seriously, the neck pickup sounds awesome for cleaner, mid-neck chords but it just is muddier. That's by design. You can turn the tone all the way up, and scoop your EQ if you have one. But your best bet for power chords on a Les Paul is always the bridge pickup or combo. Attack closer to the bridge than the pickup for a brighter tone too.

I would've given a price range but I had no idea what the prices on decent amps can range from. As for trying amps, I wish I could but the closest place I know of to do that is the pawn shop, and their selection is pretty lacking at this time. I'll check in from time to time though. Judging by what you said though, Marshall does seem like the way I'll be trying to swing. I like the distorted, old rock sound, part of the reason I chose the Les Paul, other than the fact they are gorgeous. Speaking of Les Pauls, I've already decided the next one I'm going to buy, a Gibson Les Paul Studio in Manhattan Midnight Blue. After that I'll hold off on guitar buying since that'll make 3 Les Paul's in a span of 3-4 months.

I have to correct an error in my previous post, I was indeed using the bridge pickup on the Les Paul. As for the sound, I also fixed that. I didn't realize my D string had come out of tune and I feel even more like a beginner for not noticing it. After tuning it back up, I got that sound I love.