Combi's seem to be recommended a lot, possibly due to the fact they are easier to install, but are not necessarily suitable for everyone. Smaller combi's may struggle to fill a bath, and most will not feed two hot outlets at once. (If someone is showering then turning the sink tap on to wash up may affect the shower...) Most installers have their preferred boiler manufacturer, but as with most things you pay for what you get. General consensus on this forum is Ideal's can be pretty poor, however any boiler will fail if badly installed onto a dirty system.
New back boilers are available, c/w an electric fire front, however like any new boiler, they need a means of draining the condensate discharge to outside. (Can be pumped, depending on layout of property etc.) Alternatively, there are boilers which will work with your existing system, some alterations to the pipework would be necessary, but would allow retention of the hot water cylinder if preferred. As John has said, combi's have more to go wrong, so bear in mind if a combi breaks down, you lose heating and hot water, whereas if a cylinder is used then an immersion heater can be fitted to provide backup for hot water in the event of a boiler breakdown, and an electric fire would heat a room if necessary.
