Inboards can be either petrol or diesel. They will generally have an alternator that will charge all your batteries. Diesel is readily available. They will power a larger boat. They do take up space inside the hull. Waste heat can be used to heat domestic hot water. They make a boat difficult to steer in reverse unless there are stern drives fitted.

It comes down to choice, what you intend to do with the boat and I suppose and if buying second hand, what is available at the time. I have no experience of diesel heating but it seems quite widespread on the "cut" so it must be OK It has one advantage in that it can be run from the main fuel tank so no gas bottles to change and diesel is readily available. There were issues I believe with noise of operation on some diesel boilers so this should be borne in mind.

Solid fuel stove are traditional and can have back boilers to heat radiators and with the addition of a pump can heat the domestic hot water. I would imagine in summer using a solid fuel stove for hot water would not be good as the cabin would be heated by default. If you used to hate cleaning out the grate at home then they may not be for you. A solid fuel stove if positioned correctly would probably heat a 50' boat adequately on it's own. On QE2 (40') the stove does heat the whole boat but with it being at one end to get a reasonable temperature at the opposite end to the stove, the end where the stove is does get a bit too hot. Solid fuel stoves are (like any fire) not as controllable as central heating. You need to carry the fuel somewhere and then there's the cleaning. I personally would not be without my stove I find the glow reassuring and the flames hypnotic. They also provide more heat than you would imagine and will generally stay lit throughout the night.

Central heating either by gas or diesel via radiators is similar to your system at home. QE2 has a gas boiler and 4 rads. It works very well and provides plenty of hot water. In summer it can be switched just to hot water. It does use a fair bit of gas and of course the bottle does need replacing which always happens at the worst moment. Diesel heating does the same thing but no gas bottle. Some systems are connected to the engine so cabin heating can be produced by the engine from waste heat (free).

Again if buying second hand it will be down to what is on the market at the time. If I were buying a new boat I think my ideal system would be combined system with a quiet diesel boiler, a solid fuel stove, all linked to the engine.

Power, Again many options, but what you must do is consider what you are going to do with the boat. Obviously the odd weekend use is a bit different to living aboard. A 240v mains system is useful only if you have access to shore power. If you do then you can have all the stuff you have at home washer/dryer, microwave etc. Within the limits of the shore power line a 2KW immersion heater would probably "trip" a shore line. However, running these things cruising means generating your own 240v power. Many use inverters. These convert 12v battery power to 240v AC. They are expensive and take a real toll on your batteries. The use of large inverters requires a large battery bank and of course these need to be charged. 240v AC alternators are available to run from your engine but again these are expensive. I think you should consider what your requirements are likely to be. If you are running just lighting then 1 domestic battery would do. Start adding colour television, 12v fridge and the battery bank must be bigger and so must the capacity to charge them. I cannot go into much more detail as the options are very wide. Also if buying second hand you are back to what is available.

I would recommend you do a "power audit". What are you likely to use in day? This is measured in amp/hrs.
e.g. If a light bulb on the boat is rated at 20watts, (most equipment has it's consumption written on it somewhere) to find the current draw (amps) divide the wattage by the voltage. Let's assume the system is 12volts so 20 divided by 12 gives 1.7amps. If the light is run 4 hours a day it will use 6.8amp/hrs
If the calculation is done for all the gear on the boat you will have a good idea of your power requirements. From this you can decide whether the battery capacity is enough. Bear in mind domestic batteries should not be discharged below 50% so count a 110amp/hr battery as 55. Also you now have an idea what the charging system has to replace daily in the time you are moving.

It's actually a bit more complicated deciding if you can charge up again in a days cruise but a bit of research will give you an idea if the system will work.

Hot water is generally these days provided by a calorifier (hot water tank) it is heated from waste heat from the engine and possibly also a central heating system. I would imagine if the only way of heating the water was from the engine, you want a shower in the morning and the engine was last run the previous afternoon you have to go out on deck (presumably in night attire) start the engine and run it for an hour or so before you can shower. This would not do for me personally but it's down to preference. If there is a central heating system then this will also heat the water so rather than having to go out and start the engine with the resultant noise (which may upset your neighbours) you can just start the heating.

There are many instant hot water heaters on the cut. These are very convenient being like a domestic multipoint. Light the pilot light, turn on the tap viola! However, these have been banned on new boats by the Boat Safety Scheme so a newish boat is unlikely to have one. I'm not aware of any that now fulfil the new requirements but I bet they are out there somewhere. The drawback to these is that again you have gas consumption and of course any safety worries (fumes entering the cabin)