Couldn't you ask something a bit less contentious - I hear religion is a tame subject ! Thing is, if you ask a dozen people, you are likely to get at least 13 different answers - and some of those people will argue "quite strongly" that some of the options suggested by others are a pile of poo and should never ever ever be considered
Bernard's beaten me to it on a few things - but heed what he says about servicing. More on that further on ...
First off you need to define a few variables. What fuel options do you have ? For example, it's no good thinking about natural gas if there's no mains gas. If you do have mains gas then (at least in the UK, your avatar flag says you aren't) that beats LPG (tanked) gas or oil by a long way on cost. Heat pumps have their place, but efficiency drops off dramatically (even falling back on immersion heaters as more efficient) if it's cold enough.
Will you have any solid floors ? Will you be having bare floors (wood, tile, stone) ? Will you be having thick carpets ?
What's your budget like ? There are some very good options out there, but some of them "cost a bit more" than others.
And a bit factor - how much space do you have ?
So, here's what my preference would be ...
No combi boiler. I don't like them, and I would not choose one unless there were good reasons for not using something else. They are a massive (and I mean REALLY massive) compromise as they have to be high power in order to give something resembling a decent flow of hot water, but in most situations that means they are massively over-powered for the heating load. So poor at hot water (limited flow rate - bath takes ages to fill sort of thing, not to mention the shower stops when someone turns a hot tap on), and poor at space heating as they are generally very badly matched to the load due to oversizing.
Thermal store - this gives you a good neutral point to connect all the sources and sinks to. It also gives you mains pressure hot water without the complications of stored hot water under pressure. It needn't be large if you will be having a boiler and don't need much heat storage, or it can be larger if you want to take advantage of (eg solar thermal).
This is probably the most contentious part - many "plumbers" will do that special sucking through teeth that they must teach at plumbing school and tell you how crap they are, how they cannot ever work in any situation, etc, etc. And then they'll tell you that a combi boiler is the best thing since sliced bread.
To that you connect your heat sources - gas boiler, oil boiler, biomass boiler, heat pump (air source, ground source, water source according to your resources), solar thermal panels, wood burning stove, ...
And then you connect your sinks - heating.
If you have any bare floors then UFH makes them much more comfortable - this is more so if they are stone/tile which are darned cold underfoot if you aren't into wearing thick socks and slippers all the time. This is another of those argumentative points - there are those of the opinion that UFH does not and cannot provide sensible heating (despite the observable fact that it works for a lot of people).
But if you have thick carpets, then UFH becomes "less effective" though it can still give a psychological feeling of being warm by keeping feet warm. So that then brings you back to radiators.
I've been giving some idle thought to how to combine the rapid response of radiators with the comfort underfoot of UFH. Most of the schemes I've dreamt up involve a separate UFH pump and loop in series with the radiator supply or return so the TRV on the rad effectively throttles the heat input to the UFH. That means a lot of kit (expensive) and space required.
Or you can have just radiators and/or just UFH in parts of the house. Then will run nicely alongside each other without interference due to the neutral point provided by the thermal store.
In my rental flat I put in a thermal store. The old combi was being a PITA and there are flue issues that mean I'm not keen to replace it. The tenant is very happy with it, the boiler has been fairly reliable since, and the system is really quiet since the rads can run with a modulating pump at a variable flow rate once they no longer have to fit in with the incompatible requirements of the boiler for a fairly high minimum flow rate.
I did a thread about the install over on
the Navitron forums (if you ever head there, don't ever criticise wind or be pro nuclear - over there you get banned for thinking that nuclear has any part to play or that wind power isn't the answer to all our needs)
Of course, if you have no space and no budget - then fit a combi. Developers love them as it means they can reduce the size of the shoeboxes they build by the size of the airing cupboard