That is an interesting question with the answer highly dependent upon your overall goals, budget, and current heating fuel (i.e. gas/oil/propane/electricity).
- Since they are hyper-efficient, and provide air conditioning as a "side-effect," I almost always steer people towards ducted or ductless heat pumps.
- However, heat pumps tend to not function well when it is below freezing outside and also would require a totally different infrastructure/distribution system than the existing boiler/radiant combo.
Start by checking your building envelope
Regardless, I would recommend working with a local building science expert (AKA energy auditors or home performance contractors) to help develop a reasonable scope of work. Most likely, it will first include doing some air sealing and installing additional insulation unless that has all been done recently to modern standards.
After you have ensured good thermal performance of your building envelope (i.e. walls/attic/crawlspace), then it will be time to make a decision about heating system options.
Will a heat pump be feasible for you?
I would always say it is worth looking into the cost and potential functionality issues for a heat pump system.
If that isn't feasible, then I would recommend a condensing gas boiler rated at 0.96 AFUE minimum. Click here to read about them on the Energy Star website.
Beware the new technology premium
And yes, the greener solutions most often pay for themselves; however, the greenest solutions often have a "new technology" premium and frequently have installation issues since they are typically new to the market.
Thus, in summary, I would recommend working with a local certified building performance contracting company to develop a scope of work that includes hyper-green, but not greenest, solutions such as air sealing and insulation in conjunction with a new condensing boiler or heat pump driven system.
For more information:
Read Randy Potter's Q&A "I can't afford geothermal. Is an air-to-air heat pump my best option for heating?"
Also, check Richard Parker's Q&A "Can you help me select a high efficiency furnace?"