What is a Mini-Split? Should I consider?
 
Well yes and no!  Or it depends, right?  A friend actually approached me with that very question.  He has a two-story, open architecture, house, actually three-story given the basement shop, all heated with wood.  (Biomass these days, right?)  Here, there might be two right answers.  If installed to supplement the wood stove then, yes the mini-split could work well.  But if it is to be the main heating system, maybe not. 
 
First of all, what is a Mini-split?  It is a heatpump for sure.  One might call it an air to radiant. Generally on the smaller side with the outdoor air unit and the indoor radiant unit or “head”.  Sometimes there might be several heads, but that’s the basic unit.  While there can be air flow across the inner head, there is no ducting so heat is very localized.
 
Efficiencies can be good in cooler weather to not so good in cold weather.  In cold weather there are two things acting against it.  There is not so much heat in the air and the indoor unit is calling for more heat and therefore higher temperatures both pushing down the efficiency.
 
Generally there is not a backup heating element as we have in the air-air and air-water so sizing the unit for worst case conditions is difficult.  But if a house been designed with a mini-split in mind, with an open house layout and with low heating loads, it can work.  To the mini-split’s credit, most have variable speed refrigerant compressors so that over sizing is not a major issue in efficiency, just cost.  With the mini-split, the main issue I see is the inability to direct the heat where you might want it, say the bathroom.  And I find the “head” mounted on the wall less than attractive.   
 
Back to our friends.  They installed the mini-split and are very pleased with it, using it in the fall and spring to knock off the morning chill in the kitchen while having coffee.  They might not even start the woodstove on days when the sun is out.  Even mention a savings of some fire wood for not much in electrical useage.
 
The mini-split also served another purpose. It replaced a build-in electric heater wall heater that was used to keep the house from freeze up if gone in the winter.  While the mini-split may not maintain temperature in winter, it can keep the house above freezing in our climate. 
 
Bottom line, the mini-split can add value by recognizing its limits and designing accordingly.

Geothermal Heat Pumps, are they worth the effort (and expense)?
 
First some terminology:  Geothermal is better termed “Ground Source”.  Why?  Few of us actually have a Geothermal feature such as a Geyser or Hot Springs to take advantage of.  But we do have ground or in some cases maybe a lake or a pond from which heat can be extracted. 
 
Properly designed a Ground Source heatpump can be very efficient, particularly when coupled with a low temperature heating system such as hydronics.  Possibly a Coefficient of Performance (COP) of 5:1 (5 units of heat energy for every unit of electrical energy to run the heatpump compressor).  To compare, an air to water heatpump might have a COP of 3:1 and air to air maybe a COP of 2:1. 
 
The COP for the air units are Overall Estimates as “Heating” must be supplemented by Restive Heat.  In the Air to Water this would be an Electrical Element in the water buffer thank.  This is essentially the same as the electrical element in your electric hot water tank.  This supplemental heating is necessary because the air-source heatpump’s heat output drops with decreasing air temperature, just as the heating load for the building increases.    But this does drive down the efficiency or overall COP of the air source heat pump.
 
The familiar Air to Air heat pumps operate on the same backup principle.  In this case there are electrical surface elements within the blower housing that cut-in to maintain temperature as the heatpump output drops due to lowering outside temperature. 
 
Of the two styles of heat pumps, the Air/Water heat pump will have the better COP because the heating temperature required will be lower than the Air/Air.  An in-floor radiant water system may only require 90F water to heat the house.  While for a Forced Air system it is not uncommon to require 120-130F at the heat pump heat exchanger.
 
The answer to the original question?  It depends! 
 
Properly Designed can be a very big question for the ground-source heatpump.  While I claim no expertise on designing these systems, there have been enough failures to use caution here.  In particular, the ground loops might be undersized to minimize construction costs but at the expense of the system.  The water to earth heat transfer through the relative thick HDPE piping is not a great heat transfer mechanism at best.  Or another issue, the hydraulics of the pumping loops have not been properly evaluated.  Here I do claim some expertise.  Pumping horsepower directly offsets against system efficiency and should be fractional horsepower requirements.
 
Heating Load is always an issue.  Minimizing heating load goes a long ways toward decreasing the need for extraordinary solutions.  Ground-source heatpumps being one of those.  Note:  See other discussions on minimizing heat loads.
 
Equipment Availability is the final issue.  There are a number of manufacturers of Water-Water heatpumps and many-many that manufacture Air-Air heatpumps but very few that offer the air-water heatpump which might be the best option in terms of return on investment.
 
What a discussion, right?

Heat Pump or Boiler – Which should I consider?

To a large degree, it depends on preference and what fuel options are available to you.  For instance if Natural Gas is available it is hard to argue with the boiler option.  Price of fuel is reasonable and regulated.  However if the fuel choice is oil or LPG, where price can vary with the world markets then maybe the heatpump is a consideration.  The heatpump can be more expensive to install, but they are very efficient in the use of electrical energy. And heatpumps have the added advantage of providing summer cooling.
 
The Answer:  It depends!  Preference, Fuel Costs and last but not least, Heating Load requirement.  Minimize the heating load by building tight and insulating well, then equipment is smaller (and less cost) and other options can be considered.

In your view, what is the best heating system?
 
Boy, that is a tall order.  First is the heating envelope, build it tight and insulated well.  But both of these can have problems:  “Tight” still requires ventilation which points toward a Heat Recovery Ventilator, another piece of equipment to install and maintain.  “Insulation” must be well thought out to keep moisture from condensing in the walls.  In the old R11 and even R16 packages, the wall never cooled to the condensing temperature of water.  Of course that came at a price, heat was moving to the outside through the wall.  Next is a look at the available energy sources at the site.  Is natural gas available, is there solar potential?  Then we do our Manual J load calcs to determine our heating requirements.  (Note: no Rules of Thumb here, which leads to oversized equipment, never efficient.  Make sure that your heating contractor does the HVAC calculations that takes into account all your construction efforts above.)

It is only then that we look at heating equipment.  The choice is endless but we have done our best to minimize the size and therefore cost.  Cost not only in purchase but in operation.  As you might guess, I lean toward hydronics.  Too many advantages in my mind to ignore.  Quiet, comfortable, efficient, long life.  Actually with a few plumbing tools and a good design, the systems are not that difficult to install.  To me hydronics simplifies the whole heating equation from space heating to domestic hot water.  If a boiler is the choice, domestic hot water needs might be an Indirect Hot Water tank where the boiler is the heat source through an internal (or external) heat exchanger.  One heating device serving all purposes.  “The best heating system?” A simple answer to a complex question.

ps: Heat Pumps (Hydronic – Water Style) can also meet Domestic Hot Water needs with the addition of a Desuperheater Exchanger but that is a subject for another post.

What do you think about the Tankless Water Heaters?  Never-ending hot water sounds great but it seems like many bells and whistles to maintain.
 
Yes and Yes.  Or maybe No and No.  It does sound great but much to maintain in controls and equipment.  The Tankless Water Heater is actually a boiler and a rather large one at that.  In fact in many cases BTU/Hr rating will be higher than the boiler (or furnace) that will heat your home.  My view, a tankless water heater is a solution looking for a problem.  The only real justification is “standby heat loss” attributed to the tank type water heater.  But with better tank insulation, that justification is fast disappearing and wasn’t even real if the water heater was within the heated envelope.  There the water tank was just losing heat to the house which is heated anyway.  And the boiler?  The hot water is anything but instantaneous as the boiler goes through its purge and firing cycle, maybe just to rinse a dish in the kitchen sink. Actually many of the Tankless Water Heaters have added a tank just for this purpose; while small, are we back where we started?