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A lot of this information is available here and there on the 'Net, but it's never been condensed, so here it is.
Tuning
Standard E-tuning sucks. To play right, an electric guitar has to be tuned to C or lower. This is usually just two tones down or three tones down, etc. Instead of tuning a string to E, tune it to C, etc.
C Tuning:
String 1: C, 256 or 512 Hz;
String 2: G, 191.8 Hz;
String 3: D#, 152.2 Hz;
String 4: A#, 114 Hz;
String 5: F, 85.5 Hz;
String 6: C, 128 or 64 Hz.
The differences are due to guitar brightness, e. g. a brighter guitar might have a low string fundamental at 128 Hz rather than 64 on a bassy/darker one.
Here there is a list of some more tuning layouts.
Locking Nut
...is a requirement. There are two benefits: stable tuning and a cleaner sound, as locking nuts are made of metal, not plastic. Plastic nuts give off an ugly plastic-barmy-tube kind of tint.
Nut Height
Ideally this is as low as possible, but a nut can be raised somewhat to make strings play sharper (and out of tune on the lowest two-three frets).
Bridge Height
The lower the bridge, the better the sustain. The higher the bridge, the sharper the attack. Most players drop its height until strings are starting to thrash on lower notes. This doesn't matter as much on an overdriven electric guitar as it would on an acoustic as pickups sense strings and there is no soundhole to amplify thrashing. It does matter for clean/chorused playing though, as the thrashing will be audible, so raise the bridge just above thrashing threshold.
String Calibre
At least .012 sets make sense, better .013. Low strings might be harder to bend on higher notes, but thicker strings are more musical, easier to play correctly, and they don't go as sharp/screechy as thinner sets, thus string attack is more even and plucks are more in tune. Thicker strings also give off more of a "string" sound rather than vibration amplitude, as thinner strings do. They also have a slower vibration amplitude and thus give off a bigger sound.
Pickup Height/Alignment
Ideally each pickup pole is aligned to each string. In the real world that's not always possible. Unless the (rare) pickup has individually adjustable screws, the only real tweak is adjusting pickup height.
The higher the pickup, the more of a string tone and less wood/body resonance (it's more delayed and lower in the mix). This is sometimes called "hot pickup" and basically the waveform starts getting squashed and gets more bass in it as the pickup moves closer to strings.
The risk here is, if the pickups are too close to strings, they will start dragging the strings down by sheer magnetic attraction. This likely doesn't matter as much for thicker strings in a lower tuning, but the effect is there and it can affect tone/sustain and perhaps even ease of playing and sustain at higher frets.
Pickups can also be adjusted asymmetrically, to boost either the treble or bass strings.
Straplocks
Get them ASAP, otherwise there's always a risk of guitar slipping out of its strap, with tragic consequences.
Intonation
The tiny saddles on a bridge are there to intonate strings. That is, to insure each note is more or less precise, not too sharp or flat. In practice 100% accuracy is not achievable, but you can at least get a 20-cent or so accuracy for each fret with some tinkering. The saddles are moved with a screwdriver, altering effective string length. The trick here is retuning, tweaking, and getting the right length for each string. When is it right? When the note produced by an open string is as close as possible in tuning to the note plucked at fret 12 (and 24, if the guitar has enough frets).
Picks
There are plastic picks and there are metal picks. Metal picks are generally better, unless a duller, darker tone is needed. Some good picks are Dunlop Teckpick (bronze and steel) and Dunlop Tortex (thick plastic). There also are curved tiny plastic Speedpicks, which are great for fast playing. Oh, and Brian May loves to play with a coin - he says it's better than any pick (it's a thick metal pick basically, the sound is bigger and fuller than with a thin metal pick).
Metal picks give a sharper, brighter sound. They are better for darker Gibson/Epiphone guitars and the like (SG, Les Paul derivatives too, not necessarily made by Gibson/Epiphone). With a bright tone capacitor/pickups the difference is less, however when recorded metal picks do produce a sharper, fresher waveform.
Steel is sharpest/brightest, bronze is somewhere in-between plastic and metal (rounded, balanced sound), and plastic is dullest/darkest.
Valve Vs. Transistor Amps
Valve amps are better, that much is common wisdom. The real reason why they are better is because they have an overall better dynamic response, which is more even in the higher frequencies (above 3 KHz). A sine sweep won't show this, but transistor amps tend to lag in the high frequencies/treble, with sticky HF harmonics. Valve amps are quicker in the high frequencies and they distort on even harmonics, not odd. Basically valve amps draw treble (and therefore size/dimension/contour) better than transistor amps. The main snag with valve amps is low-quality components (slow/high-ESR caps, as an example) and poor wiring/shielding (eating away quickness and crispness) and last but not least, common audio valve designs (12* family) aren't that sharp.
The advantage to valve amps is, they play a lot more musical and record better, a valve amp doesn't have to be driven as loud to get a good definition, and its better contour/treble insures guitar stands out better with less relative mix loudness. This is because dynamics and treble are essential for presence and dimension and instrument definition/separation, and the same applies to non-guitar audio amplifiers - transistor amps are inferior to a well-designed modern triode or pentode amplifier. So even if a valve amp is more power-limited, it'll play louder/crisper at less power than a transistor amp. And with smoother, cleaner, better treble, which defines clarity and overall fidelity/definition. Well all right, high midrange in an electric guitar cab speaker's case.