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LS1 engine - check the "Engine Swap" forum sticky section. Not a bolt-in by any stretch, a used engine/transmission installed by a competent shop will run you at least $6k, probably more.

Crate - The low-end LS1 will run you $4900 plus shipping. Other crate engines are available - check www.sdparts.com for examples.

Any particular reason you want a "crate" engine? Most transmissions are rebuilt rather than "crate".

 

Hmm, this really, really depends on how much money you can afford for this, and the time-frame in which you have to work. While the LSx is great engine to drop in as it is powerful and reliable, it will set you back quite a bit and will require several new parts to adapt.

Depending on the current condition of your wiring and supporting components with your car, it may be easier to drop in a stock replacement for the 305 since speed is not an issue. The main advantage to this is that you will not have to modify any components to make it work.

If the problems you are encountering are a result of hacked wiring, bad sensors, or an otherwise failing electronic system, the full replacement of it may be best to ensure reliability. The LSx would take car of this, but also requires further modifcation as mentioned earlier.

If you have the time and money, the LSx would be beneficial, but if the only problem is the drivetrain (considering that everything else is fine), stock-spec replacement items would be the easiest to drop in.

 

If you're on a tight budget, drop a new base GM longblock (~$1200) in there with your induction system. Or better yet, for about 40 more horsies, go with a new L31 Vortec longblock (~$2200) topped with a Vortec intake base.
If I needed a new/rebuilt trans, I'd get one from CPT (Carolina Performance Transmissions). He's been building some very durable units, holding up well in 2-ton ImpalaSS's on the strip and street. For your application, I'd guess about $1200 with the warranty.