All batteries provide electricity, and all chargers provide electricl output, so it can sometimes be a bit hard to decide which is the most appropriate...
There are a few figures which describe batteries which might help you compare things:
Voltage - the 'pressure' at which batteries provide electricty. Your radio needs around 5v (provided by the BEC), your motor needs 6-12v. A 7.4V battery is fine.
Capacity - the amount of power in a battery, measured in amp-hours. 1.5 (your 1500 ma) is ok for a small radio. I would like more for your sail winch, and you defintely need more for your motor if you want to run it for any length of time. I might suggest 4 Amp-hours (4000ma) at a minimum, but a lot depends on how often you want to use it. If your motor draws, say, 3a, then you would have less than 30 mins run time on the motor alone with no radio. Might be ok if you use the motor very infrequently, but I would like a larger safety margin.
Discharge Rate - how much power the battery can put out at one instant - measure in Amps. This is often not well understood, since batteries are often designed fo two quite dissimilar functions: putting out a lot of power rapidly, or putting out a little power for a long time. You can pick a battery with high voltage and a lot of power, but if it puts it out very slowly it may not run a high-drain unit like a motor very well. You probably need something that can put out a minimum of around 15A (start-up current) to run an M500 effectively. Which your 1500ma Li-ion should do...
Lead Acid batteries typically have good capacity, good voltage and a fair discharge rate. They are heavy and bulky, but that may not be an issue for a big yacht.
Ni-MH or Li-Ion are a good choice for your application - Li a bit more expensive than Ni.
Li-Po batteries are typically optimised for light weight and high discharge - they can also be a bit temperamental to charge. Your application does not need this.
I would consider your requirement in the light of the above info, then phone up Component Shop and ask for their recommendation.
A multi-purpose charger like the iMax B6 (and its clones) will usually offer multiple connector options. I would re-iterate Stavros!'s advice to take the battery out for charging - It's a good idea to disconnect all batteries if they are not being used to avoid the dreaded 'Black Wire' disease, and they should be regularly inspected all over for signs of damage, corrosion, etc...