Congrats on the new guitar
I love LTD too. I own two - an EX shape and the F type. LTD are the cheaper (ie affordable) spinoffs from ESP. For what you pay, I've found them to be much nicer than an Ibanez equivalent. This was a few years ago though, maybe things have evened up, or changed, but just looking at your guitar, I'd say the standard is still right up there.
I used to sell guitars and have been playing on/off 7 years. First of all, any (solid state) guitar amp up to about 50W will be very useable in a bedroom situation without bugging your family (in a house that isn't titchy small). You wouldn't want much louder anyway. With tube, say 30W, as they are usually louder than a solid state amp rated at the same wattage. The Roland cube is a good little unit, they sold pretty quickly where I used to work. There are better amps for the money though. An amp of this size will be fine until you want to jam with a drummer, then you'll probably have to double the watts (for rock music at least).
patalp is 100% correct. You should definitely take your guitar to a local shop and plug into a Fender tube amp, a Mesa Boogie Rectumfrier (
), a Marshall Valvestate (dodgy tube-a-like solidstate amps), and also a Peavey. Basically try out as many as you can, all price ranges, solidstate and tube. Make sure you bring YOUR guitar, and don't use one from the shop, it's irrelevant what a guitar sounds like with an amp, if it's not the guitar you'll actually use with the amp. Make sure u know what the amp is when u try it, and compare directly if u can. A good salesman will let you. Guitars/amps/effects are even MORE personal preference than Head-Fi stuff, because while it's good to have a rig that will make you sound like Metallica or whatever your fave band is, it's MORE important that the rig gives you some freedom of tone to play around and hopefully come up with a sound you really like.
When you try the amps, make sure you don't just set the guitar to the bridge pickup and forget about it - pickup choice is a HUGE thing to give variation in tone. On a (in the grand scheme of things) treble heavy guitar like most of the ESPs/Jacksons/Ibanez, you'll probably want to use the middle position of the pickups, so you get a bit more body into the signal you're feeding the amp. Otherwise everything will sound more trebly and gutless compared to what the amp can really do. On the other hand, Fenders, Gibsons and Gretsches will be the opposite, they have a very full/warm sound, and (all other things equal) will portray amps as being warm compared with your guitar plugged in.
Make sure you test how loud the amp can go without breaking up (although bare in mind that some are designed to break up smoothly with harder picked notes, ie tube amps). Also, since you are going to be playing in a bedroom situation, play for a while at bedroom volumes and check it sounds "fun" etc... Many amps are designed to run within 50>70% of their volume range to really "open up", just as some headphones and amps seem to perform better up louder/quieter. I have a 100W amp in my room, and when played quietly it sucks. Played loudly (as I do), it comes into its own.
Yep, the Pods and those other units are all pretty nice. Personally, I bought just one distortion box I loved the sound of, and learnt as much as I could for the first 2.5 years before getting a Boss GT6 and being done with it (but the distortion on it bites compared to tube and even my amps built in distortion).
If you buy a multieffect straight away, you could just be presented with so many options that you don't know how to use them all properly in combination and might throw your hands up in disgust, I saw so many ppl do that lol. If you DO get something, I'd suggest one of the entry level BOSS multi-effects.
If you can tell the difference between (solidstate) SS and tube and refuse to use SS, you might have to use a convoluted setup with a multieffects to retain tube overdrive and use it in combination with the digital effects. Last time I looked, several of the multi-effects units claimed to have tube or tubelike distortion built in, but they were all a joke. If you want tube sound, you'll really need a tube amp, or at the very minimum there are one or two stomp boxes which do/did it well. Or you can get a unit like the Boss GT6 which has a FX out/return which can be used in combo with a tube amp.
Also, I didn't check out your guitar on the LTD site, but if it has passive or active pickups, that will make a pretty big difference too. I'm gonna take a wild guess you like metal/rock, so the guitar is a good choice. Especially if it has active pickups.
RE the guy who asked about fret buzz: 1) get it setup by a pro. Should take 30 mins maximum. 2) Some cheaper electric guitars will always buzz unless you set the action unplayably high through bridge/saddle/neck adjustments. Some guitars like Jackson/Ibanez are also purposefully setup really low so the guitarist can play faster, at the cost of having a bit of buzz. In a loud concert environment this isn't really a cost though.
BTW: Changing the strings on a Floyd-rose licensed (pretty sure your's isn't a real Floyd-rose, but it hardly matters these days) is a "fun" experience lol.
By the way, unless you wish to damage your hearing, I REALLY recommend against practising guitar using headphones under any condition. In my opinion, guitars output a very specific frequency range that is much more narrow than music. If you ever see a mixer's desk and dial out everything but the guitar, more often than not the majority of the signal only ranges from ~100Hz to ~a few kHz. There is the tendency to turn up the amp/headphones to try and fill out the sound, and you'll kill your ears. Also, I wouldn't use any "hifi" style headphones to plug into a guitar amp. When I hear un-compressed, un-limited guitar sound with volume spikes all over the shop, through "nice" headphones, I cringe and wonder if it's having some ill effects on the cans.
It may have no real effect, but I don't do it anyway , mostly because I believe: headphones + raw guitar = deafness.
Check out:
http://www.harmony-central.com/
http://www.guitarstuff.com/lessons/lessons.html
http://www.guitargeek.com
And don't feel that you need to get lessons to get better. There's heaps of stuff on youtube and free online. However, if you ever experience pain while playing, you may well be using poor positioning, so maybe ask a friend who plays, they will most likely point out what you're doing wrong (trying to learn Master of Puppets as your first song will do it
).
Whoops... I forgot how much I enjoyed telling people the ins and outs of their first guitar
But now I can see why some kids just had a stunned look on their face and just relied on what I recommended they buy
I like to think I gave good advice though lol
Guitar Pro is OK, although a lot of the tabs on the net aren't very good/accurate, and should only be used as a starting point. It erks me when someone has tabbed out a song in completely the wrong tuning. You'll learn a LOT if you try to work stuff out for yourself once you feel confident.
Since you can read music, that'll make guitar easier to learn. It's all just maths. And just remember, if it sounds good, it IS good. Same as with Head-Fi, but MORE so, because it's ALL personal taste, sometimes awful distortion is the desired effect in cookie monster rawwwwk n rawwwwwwwwwl hahah \m/
That guitar looks very similar to an ibz rg. just smoother horns. 
Linear Mode
