By far the largest range of very high efficiency boilers are gas/propane. Propane can cost more than oil. You can probably get propane if you have room for a tank.
But with gas you can get a modulating condensing boiler. Many of these have almost no water retained in the boiler itself.
What does this mean?
Modulating - the boiler can fire at a variable rate depending on multiple factors such as heating/DHW demand, outside air temp. This means that a boiler may run at 20K BTU for light heating and with relatively low temp water. Cranks up to max rate of the boiler (e.g., 100K BTU) when demand is high (e.g., DHW).
Condensing - boiler condenses the exhaust gasses to recover latent heat. Water comes out a drain and much less goes out the vent (which can be PVC). When this is happening the boiler can do about 98% or so efficiency. The higher the water temp the less effective this recovery is, but it will still be quite good. I think the magic number is around 135 or 140 degrees but don't quote me. When my boiler (WeilMclien) is doing the house heating the water temp is seems to be running from about 90 degrees to about 115. I store DHW in the SuperStor at 140 degrees. Less temp runs the risk of Ligeonella developing in the tank. A tempering valve is necessary for DHW either at the tank or at each fixture. Each fixture is best in my mind because it gets the pipes hot. But it costs more and has more pieces to break. Some fixtures have this built in. The temp of water used for heating is a function of the design of the system emitters (in-floor, radiators, air exchangers). In floor should use the lowest temps, followed by radiators.
Little water stored in the boiler jacket and heat exchanger - you don't have the problem of keeping that water hot in the summer. I believe my boiler is less than 2 gallons plus some piping to the DHW tank.
Maximum advantage accrues with smart controls. The boiler can do some of this by itself but an external control system is much smarter and adapts to conditions better. My feeling is that Techmar is the gold standard for these controls.
It ain't cheap up front. But it may pay for itself rather quickly depending on existing system performance.