I can help some of the way here.
Firstly, the type of battery doesn't matter to the speed controller or the motor - it's all volts and amps when it gets that far.
The Sanyo is, at an educated guess, 7.2 volt, 4000 mAh (milliAmps per hour) based on the info you provide. Therefore the closest Li-Po you could get would be a 2 cell (2S) 4000 mAh - this would give you 7.4 volts nominal.
In terms of current draw, the limiting factors are what the motor will draw, what the ESC/Speed Controller can handle and what current (Amps) the battery will supply. Li-Po's will supply a LOT of current in a very short time frame - that Turnigy you mention, rated for 15C will supply 1400 mAh for one hour - or can supply 15C times 1400 mAh in a burst. That is way more than anything scale (probably even fast electric types) would need. If the hobby shop says the speed controller will handle up to 25 Amps then a 20 Amp fuse either side of the controller would protect the controller you have. Electronic Speed Controllers can be sourced that handle more than 25 Amps. Action Electronics I believe, and Mtroniks, have ESC's to handle this. Electronize may have - I'm not sure about those. See the Traders pages for links for these, or just Google...
As for BEC's - some will recommend for and others against. Mtroniks ESC's have a BEC built in. I don't think that the Action ESC's do - someone (probably several!) people will correct me if I'm wrong. No idea about Electronize. You can buy and install these separately from the ESC/SC anyway. And I would recommend a Li-Po guard to protect against over-discharge of the Li-Po too. I imagine that E-Bay or your local equivalent will have these, if not your local hobby shop. Presumably if you are thinking about Li-Po you will know you need (or already have) a suitable charger.
Any other advise will need some detail about the boat you are putting the motor/ESC/battery combo into and others more knowledgeable than I will likely assist. Details of the prop will be a requirement - this affects the current draw (amps) of the motor, as will the type of hull displacement or planing - photos work well :)
HTH!