I am with chenks. A three box solution is the way to go. It is also about placement. The modem really needs to be very close to the wallsocket for performance - and in fact if the wallsocket is in the right place then it should be moved to the wrong place in order to shorten house-internal wiring as much as possible and reduce interference pickup inside the house. The length of cable from the outside world to the wallsocket should be as short as possible. And the modem-to wallsocket cable needs to be extremely short to get the last ounce of performance.
However, a wireless access point (WAP) needs to be positioned in the right place so that it helps give good coverage. And if that is it enough, you should have additional WAPs parked wherever you need them. So the actual physical split is between the positioning of modem and wireless kit. Excellent wireless kit always needs to be bought separately, you are not going to get it in random combination wireless routers. 802.11ac-wave-2 beamforming WAPs have longer reach because they can form a jet if energy pointing in one direction towards a particular station they are talking to and they have other clever tricks too. 802.11ac wave 2 is superb.High spec WAPs behave better in a crowded environment where you have neighbours using up a lot of frequencies, because they can use a lot of 5GHz channels, not just the very overcrowded 2.4GHz band where there are only 3 distinct 20 MHz non-interfering frequencies/channels, or at pinch 4 if everyone is cooperating and all WAPs including neighbours are carefully positioned on the correct frequencies. The 5 GHz band has a lot of 40MHz channels available, double the speed, less range, or 20 MHz channels can be used and twice as many of them. So no interference from neighbours if things are set up right. Rubbish wireless routers do not have 5 GHz at all, or may not have twin radios so they cannot run in both frequencies simultaneously.
As for routers, if one does what you need and has a decent firewall then that is fine. If you have FTTC then many modems are good performers. If you have an ultra long line and ADSL1/2/2+ then you desperately need an outstanding modem and a multi-box setup is vital so that you get the best modem and really good wireless.
So I am with chenks, it is not about fancy features at all, it is about high speed DSL (excellent modem and physical positioning) and very high speed wireless LAN plus excellent coverage (high spec WAP and good physical placement or several WAPs).
[Moderator edited to fix a few typos caused by auto-correct doing the wrong thing!]