A particular type of crash causes the game to hang on the world loading screen for a while. Try resetting your pack and allocating more RAM.
Tekkit originally started out as a multiplayer version of the "Technic" pack, which as since been retired due to the singleplayer-multiplayer merge of Minecraft 1.3. (In case you don't know, Minecraft 1.3 and later clients run on a server under the hood on singleplayer. This forced all mods to be multiplayer compatible, so only one pack was needed.) The team chose to keep the Tekkit name for the main tech-mod pack, maybe because the Yogscast had brought a lot of attention to it, or maybe it just felt more unique. Long story short, any of them can be used for singleplayer.
Tekkit is the newest, and the only one that will be updated. Minecraft 1.5 currently, will be updated to 1.6 and beyond once all the mods and the launcher update.
Tekkit Lite is the second youngest, running on Minecraft 1.4. It will no longer be updated, as Industrial Craft 2 and Redpower have been dropped and unfortuantely formed an integral part of Tekkit Lite.
Tekkit Classic, formerly known as Tekkit 3. The oldest (hence "classic") tekkit pack, it runs on Minecraft 1.2. It's fun if you liked the Yogscast's Tekkit series, or like Equivalent Exchange 2, but other than that it really has little going for it other than nostalgia.