good computer for chess engine?

Hi,

I am going to buy a computer (laptop probably) soon. I would like it to be strong enough to do good analysis using the chess engines that are out there.

What are the things that are important to a chess engine so that it can work fast and well? I have heard number of cores (2,4 etc) matter. Is that right? What about RAM?

Please let me know in plain terms as I have no idea about computers.

By the way, I see that certain engines (e.g. Stockfish) have 32bit and 64bit versions. What is the difference? Is the 64bit a faster engine?

On a final note, what is an adequate depth to look at when considering an engine's calculations? On the chessbase cloud I see most people stop the engine analysis after depth 30 or so.

Thanks