How to increase sustain
If your guitar doesn't have much natural sustain, then adding a compressor will be of limited benefit. A compressor can only bring up the level of a signal; if it doesn't get enough signal (i.e. if the note dies) then it can't boost the level.
A digital reverb unit with a good-sounding hall program might help, but there's going to be a tradeoff between note articulation and the extra "hang time" you get from the `verb.
You should get a bit of a sustain boost from the acoustic interaction between the guitar and amp. This depends upon a lot of factors including the guitar's natural resonances, the amp's EQ and volume, the reflection modes of the room and the position of your body and guitar relative to the amp.
If you hear a thump when plucking a string, your amp may be EQ'd with too much bass. A guitar is a midrange instrument. There's not a lot of useful information in the really low frequencies; cranking the bass control on most amps may not only emphasize the thumping sound, but also create a tendency toward low-frequency howling (due to body resonance on hollowbody and semi-hollow instruments). Furthermore, the added low-frequency content may interfere with amplifier-supported sustain by exciting vibration modes in the guitar in such a way that they interfere with string vibration. Roll off the bass, bring up the mids and add or reduce treble to taste.
Once you get your EQ straightened out, then you can experiment with amplifier-induced sustain. Bring up the volume high enough for the strings to howl on their own, then back it off enough to stop the howling. With a full-hollow guitar you're likely to find that the body will howl even if you damp the strings. This tells you that the volume is too high or that the EQ is wrong. Start by backing off the mid and low EQs, then reduce the volume.
When you find the sweet spot for EQ and volume, notes in certain ranges will sustain or even feel like they're going to take off on their own. At this point small adjustments in technique or your position in the room will help to damp any runaway notes.
The most important factors, though, are setup and technique. Fresh strings, appropriate action (not too low) and neck relief (not too flat), and properly crowned frets will help. Lowering your pickups a bit - especially if they're single-coil pickups - may help by reducing the magnetic attraction of the pickups on the strings. Proper fretting-hand technique will maintain proper contact with the frets - poor technique will kill sustain faster than anything. Picking technique is also important.
It may be counterintuitive, but a gentler attack often yields greater sustain. Also experiment with how and where you pluck the strings. If you need more volume, let the amp do the work.