Hey guys.

I recently bought an Epiphone Les Paul Player pack: it comes with a Les Paul Special II LTD edition guitar and what looks like a pretty low end Electar-10 (think it is solid state) amp. The guitar feels good, but I personally don't think the sound is that good. The clean tone is fine, no issues with it, but when using distortion, the sound feels way too rough and muddy.

The amp has no distortion level knob, just a button for clean or distorted. Apart from this, it has volume, bass and treble; and the guitar has a volume and tone knob with a switch for neck and bridge pickups. I have been playing around with the settings, and there are few specific combinations which seem okayish, but definitely not what I expected or what the reviews seemed to say. Is this solely because the amp is of low quality? How can I ensure that the guitar is doing fine? Please let me know what you think.

Most of the sounds you get out of your amp are because of your amp. You could be playing a much better guitar than you currently have through that amp, and it would sound much the same.

Don't sweat it for now though. Beginners generally don't have the best gear.

Still, if you worried that it is your guitar, go to your local store and try out your axe with some other amps. If you can't get sounds you like out of anything, it may well be a problem with the guitar.
Sturgeon's 2nd Law, a.k.a. Sturgeon's Revelation: “Ninety percent of everything is crap.”

Why, yes, I am a lawyer- thanks for asking!

Log off and play yer guitar!

Strap on, tune up, rock out!
The Special II has the 700T/650T pickups in it. These are pretty low budget on the scale of pickups, but not the worst that Epiphone has produced. With a good amp and a little experimentation, you should be able to get a decent enough sound out of them. I"m betting that its really the amplifier that sounds bad in this case. Most 10 or 15 watt amps dont really cut the mustard, so to speak, and small Epiphone practice amps are notorious for sounding pretty terrible. As a matter of fact, Epiphone discontinued their entire amplifier lineup except for these Electar practice amps for the Player Packs, if that tells you anything.

Like suggested above, take your guitar to a local store and see what it sounds like through a different amp. You might be amazed at the difference you will hear.
Be sure to make sure you're on the bridge pickup (switch in the lowest position). If you've already done this, turn up all the volume and tone knobs on your guitar.
Lower the bass on your amp, add some more treble, and try different volumes.
Sorry if I seem patronizing, just trying to help in any way I can.