Tekkit Classic is the oldest version, built on Minecraft 1.2.5, and is the version the Yogscast used for their Tekkit videos. The pack is mostly focussed around Buildcraft, Industrialcraft, and Railcraft as far is technology is concerned. It also includes Equivalent Exchange 2, which is generally considered to be Very OverpoweredTM.
The pack seems to run fairly well. I used it on my laptop for a long time without many problems. Probably because the number of mods is fairly low, and MC 1.2.5 still has the old 128-block build limit.
Lite is a slightly newer version - for Minecraft 1.4, I think? - that I don't know much about, other than I never really got into it and it didn't run well on my laptop. I can't help you here, I'm afraid.
The current Tekkit version for 1.6.4 is fairly bloated. It has a lot of mods that you never use, going by the "something for everyone" philosophy. Off the top of my head, it has Galacticraft, Thermal Expansion, Minefactory, Forestry, Buildcraft, and many many more. Galacticraft is the worst offender as far as lag is concerned. It also has Equivalent Exchange 3, which is an entirely new version of EE that is still in development. EE3 was intentionally nerfed by the developer.
Honestly, I would recommend Classic for using on your laptop. Once you get a proper desktop you should be able to run new!Tekkit which is probably a better experience overall. Unless you want to go down the route of insanity and make your own modpack... help me please