I don't claim to be an expert, but I have been shopping around for an LS motor for an eventual swap.
The 4.8 uses some different parts then all of the rest and should generally be avoided.
The 5.3 comes in 3 flavors. The iron-block truck motor (175lbs heavier then the aluminum one), the aluminum-block truck motor (including the first year SSR), and the FWD setup LS4 that makes 303HP ECU-Limited in the last round of SS Impala's and Grand Prix GXP's. Obviously stay away from the FWD setup ones. There's a few different HP levels on the truck versions, but not enough to make a difference. GM made some huge number of these already and this is generally the route I'm looking at taking.
The 5.7 is the "original" LS1. All 3rd and 4th Gen GM V8's are called "LS" motors, even if they aren't acronymed "LS" (think LM4, LQ4, whatever). The 5.7 came in the C5 Vette and the 4th Gen F-Body Firebird and Camaros (98-02). Also found in the 2004 GTO (regular throttle cable). The 405HP LS6 version was found in the C5 Z06 and the first round of Caddy CTS-V's. I'm pretty sure there were some truck motors and iron blocks too, but they'd all be pre-05. I didn't really look very hard at the real LS1/LS6 because they go for stupid money compared to the non-LS named ones. Good points are you can find a take out with a T56 6-Speed already attached.
The 6.0 is the "Heavy Duty" truck motor and is also available in iron or aluminum block. Also found in the first round of C6 Vette (05-07 I think) and the 05 and 06 GTO (LS2, 400HP/400TQ, drive-by-wire throttle). Found in the 2nd iteration Caddy CTS-V as well. This is the current swap king as everybody wants the GTO takeouts (T56 6-Speed or a traditional 4-Speed Auto, good for drag racing). The drive-by-wire stuff gets amusing (you'll need the pedal assembly and if you get the auto the shifter too). Luckily aftermarket larger throttle bodies bolt up so us non-ECU trusting people can use a cable. A non-LS designated 6.0 is also used in the new G8 GT (360HP or round-abouts).
The LS3 is the new "big dog" and is currently available in the C6 Vette only (430/436HP depending on exhaust ordered). It should be making an appearance in the Camaro and G8 GXP. Supposedly it can be setup with a good displacement-on-demand.
Then of course there's the 7.0 LS7 which is truly awesome, and very out of my reach.
Things to watch out for is that Gen3 to Gen4 changed the number of teeth on the reluctor wheel, so you have to stick with all the electronics from one or the other. There's a few different accessory drives (Vette, F-Body, Truck, GTO) so watch out what will fit in your bay. Truck intakes are huge but the car intake drops right in, it's just not compatible with the truck accessory drive IIRC.
If you really want to get into the nuts-and-bolts of JY LS stuff pick up the last few years of Car Craft, They did a 400HP 5.3 for stupid cheap (got the complete motor for $550!) and built a 600HP 6.0 and have had great articles on what to look for when buying a JY one.
Hope that helps!